diff --git a/dvc/api.py b/dvc/api.py
--- a/dvc/api.py
+++ b/dvc/api.py
@@ -109,3 +109,34 @@ def _make_repo(repo_url=None, rev=None):
             pass  # fallthrough to external_repo
     with external_repo(url=repo_url, rev=rev) as repo:
         yield repo
+
+
+def make_checkpoint():
+    """
+    Signal DVC to create a checkpoint experiment.
+
+    If the current process is being run from DVC, this function will block
+    until DVC has finished creating the checkpoint. Otherwise, this function
+    will return immediately.
+    """
+    import builtins
+    from time import sleep
+
+    from dvc.stage.run import CHECKPOINT_SIGNAL_FILE
+
+    if os.getenv("DVC_CHECKPOINT") is None:
+        return
+
+    root_dir = Repo.find_root()
+    signal_file = os.path.join(
+        root_dir, Repo.DVC_DIR, "tmp", CHECKPOINT_SIGNAL_FILE
+    )
+
+    with builtins.open(signal_file, "w") as fobj:
+        # NOTE: force flushing/writing empty file to disk, otherwise when
+        # run in certain contexts (pytest) file may not actually be written
+        fobj.write("")
+        fobj.flush()
+        os.fsync(fobj.fileno())
+    while os.path.exists(signal_file):
+        sleep(1)
diff --git a/dvc/command/experiments.py b/dvc/command/experiments.py
--- a/dvc/command/experiments.py
+++ b/dvc/command/experiments.py
@@ -1,13 +1,17 @@
 import argparse
 import io
 import logging
+import os
 from collections import OrderedDict
 from datetime import date
 from itertools import groupby
 from typing import Iterable, Optional
 
+from dvc.command import completion
 from dvc.command.base import CmdBase, append_doc_link, fix_subparsers
-from dvc.command.metrics import DEFAULT_PRECISION
+from dvc.command.metrics import DEFAULT_PRECISION, _show_metrics
+from dvc.command.status import CmdDataStatus
+from dvc.dvcfile import PIPELINE_FILE
 from dvc.exceptions import DvcException, InvalidArgumentError
 from dvc.utils.flatten import flatten
 
@@ -109,19 +113,30 @@ def _collect_rows(
         reverse = sort_order == "desc"
         experiments = _sort_exp(experiments, sort_by, sort_type, reverse)
 
+    last_tip = None
     for i, (rev, exp) in enumerate(experiments.items()):
         row = []
         style = None
         queued = "*" if exp.get("queued", False) else ""
 
+        tip = exp.get("checkpoint_tip")
         if rev == "baseline":
             name = exp.get("name", base_rev)
             row.append(f"{name}")
             style = "bold"
-        elif i < len(experiments) - 1:
-            row.append(f"├── {queued}{rev[:7]}")
         else:
-            row.append(f"└── {queued}{rev[:7]}")
+            if tip and tip == last_tip:
+                tree = "│ ╟"
+            else:
+                if i < len(experiments) - 1:
+                    if tip:
+                        tree = "├─╥"
+                    else:
+                        tree = "├──"
+                else:
+                    tree = "└──"
+            row.append(f"{tree} {queued}{rev[:7]}")
+        last_tip = tip
 
         if not no_timestamp:
             row.append(_format_time(exp.get("timestamp")))
@@ -373,6 +388,64 @@ def run(self):
         return 0
 
 
+class CmdExperimentsRun(CmdBase):
+    def run(self):
+        if not self.repo.experiments:
+            return 0
+
+        saved_dir = os.path.realpath(os.curdir)
+        os.chdir(self.args.cwd)
+
+        # Dirty hack so the for loop below can at least enter once
+        if self.args.all_pipelines:
+            self.args.targets = [None]
+        elif not self.args.targets:
+            self.args.targets = self.default_targets
+
+        ret = 0
+        for target in self.args.targets:
+            try:
+                stages = self.repo.reproduce(
+                    target,
+                    single_item=self.args.single_item,
+                    force=self.args.force,
+                    dry=self.args.dry,
+                    interactive=self.args.interactive,
+                    pipeline=self.args.pipeline,
+                    all_pipelines=self.args.all_pipelines,
+                    run_cache=not self.args.no_run_cache,
+                    no_commit=self.args.no_commit,
+                    downstream=self.args.downstream,
+                    recursive=self.args.recursive,
+                    force_downstream=self.args.force_downstream,
+                    experiment=True,
+                    queue=self.args.queue,
+                    run_all=self.args.run_all,
+                    jobs=self.args.jobs,
+                    params=self.args.params,
+                    checkpoint=(
+                        self.args.checkpoint
+                        or self.args.checkpoint_continue is not None
+                    ),
+                    checkpoint_continue=self.args.checkpoint_continue,
+                )
+
+                if len(stages) == 0:
+                    logger.info(CmdDataStatus.UP_TO_DATE_MSG)
+
+                if self.args.metrics:
+                    metrics = self.repo.metrics.show()
+                    logger.info(_show_metrics(metrics))
+
+            except DvcException:
+                logger.exception("")
+                ret = 1
+                break
+
+        os.chdir(saved_dir)
+        return ret
+
+
 def add_parser(subparsers, parent_parser):
     EXPERIMENTS_HELP = "Commands to display and compare experiments."
 
@@ -552,3 +625,156 @@ def add_parser(subparsers, parent_parser):
         metavar="<n>",
     )
     experiments_diff_parser.set_defaults(func=CmdExperimentsDiff)
+
+    EXPERIMENTS_RUN_HELP = (
+        "Reproduce complete or partial experiment pipelines."
+    )
+    experiments_run_parser = experiments_subparsers.add_parser(
+        "run",
+        parents=[parent_parser],
+        description=append_doc_link(EXPERIMENTS_RUN_HELP, "experiments/run"),
+        help=EXPERIMENTS_RUN_HELP,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    experiments_run_parser.add_argument(
+        "targets",
+        nargs="*",
+        help=f"Stages to reproduce. '{PIPELINE_FILE}' by default.",
+    ).complete = completion.DVC_FILE
+    experiments_run_parser.add_argument(
+        "-f",
+        "--force",
+        action="store_true",
+        default=False,
+        help="Reproduce even if dependencies were not changed.",
+    )
+    experiments_run_parser.add_argument(
+        "-s",
+        "--single-item",
+        action="store_true",
+        default=False,
+        help="Reproduce only single data item without recursive dependencies "
+        "check.",
+    )
+    experiments_run_parser.add_argument(
+        "-c",
+        "--cwd",
+        default=os.path.curdir,
+        help="Directory within your repo to reproduce from. Note: deprecated "
+        "by `dvc --cd <path>`.",
+        metavar="<path>",
+    )
+    experiments_run_parser.add_argument(
+        "-m",
+        "--metrics",
+        action="store_true",
+        default=False,
+        help="Show metrics after reproduction.",
+    )
+    experiments_run_parser.add_argument(
+        "--dry",
+        action="store_true",
+        default=False,
+        help="Only print the commands that would be executed without "
+        "actually executing.",
+    )
+    experiments_run_parser.add_argument(
+        "-i",
+        "--interactive",
+        action="store_true",
+        default=False,
+        help="Ask for confirmation before reproducing each stage.",
+    )
+    experiments_run_parser.add_argument(
+        "-p",
+        "--pipeline",
+        action="store_true",
+        default=False,
+        help="Reproduce the whole pipeline that the specified stage file "
+        "belongs to.",
+    )
+    experiments_run_parser.add_argument(
+        "-P",
+        "--all-pipelines",
+        action="store_true",
+        default=False,
+        help="Reproduce all pipelines in the repo.",
+    )
+    experiments_run_parser.add_argument(
+        "-R",
+        "--recursive",
+        action="store_true",
+        default=False,
+        help="Reproduce all stages in the specified directory.",
+    )
+    experiments_run_parser.add_argument(
+        "--no-run-cache",
+        action="store_true",
+        default=False,
+        help=(
+            "Execute stage commands even if they have already been run with "
+            "the same command/dependencies/outputs/etc before."
+        ),
+    )
+    experiments_run_parser.add_argument(
+        "--force-downstream",
+        action="store_true",
+        default=False,
+        help="Reproduce all descendants of a changed stage even if their "
+        "direct dependencies didn't change.",
+    )
+    experiments_run_parser.add_argument(
+        "--no-commit",
+        action="store_true",
+        default=False,
+        help="Don't put files/directories into cache.",
+    )
+    experiments_run_parser.add_argument(
+        "--downstream",
+        action="store_true",
+        default=False,
+        help="Start from the specified stages when reproducing pipelines.",
+    )
+    experiments_run_parser.add_argument(
+        "--params",
+        action="append",
+        default=[],
+        help="Use the specified param values when reproducing pipelines.",
+        metavar="[<filename>:]<params_list>",
+    )
+    experiments_run_parser.add_argument(
+        "--queue",
+        action="store_true",
+        default=False,
+        help="Stage this experiment in the run queue for future execution.",
+    )
+    experiments_run_parser.add_argument(
+        "--run-all",
+        action="store_true",
+        default=False,
+        help="Execute all experiments in the run queue.",
+    )
+    experiments_run_parser.add_argument(
+        "-j",
+        "--jobs",
+        type=int,
+        help="Run the specified number of experiments at a time in parallel.",
+        metavar="<number>",
+    )
+    experiments_run_parser.add_argument(
+        "--checkpoint",
+        action="store_true",
+        default=False,
+        help="Reproduce pipelines as a checkpoint experiment.",
+    )
+    experiments_run_parser.add_argument(
+        "--continue",
+        nargs=1,
+        default=None,
+        dest="checkpoint_continue",
+        help=(
+            "Continue from the specified checkpoint experiment"
+            "(implies --checkpoint)."
+        ),
+    )
+    experiments_run_parser.set_defaults(func=CmdExperimentsRun)
diff --git a/dvc/output/base.py b/dvc/output/base.py
--- a/dvc/output/base.py
+++ b/dvc/output/base.py
@@ -8,6 +8,7 @@
 import dvc.prompt as prompt
 from dvc.cache import NamedCache
 from dvc.exceptions import (
+    CheckoutError,
     CollectCacheError,
     DvcException,
     MergeError,
@@ -325,6 +326,7 @@ def checkout(
         progress_callback=None,
         relink=False,
         filter_info=None,
+        allow_persist_missing=False,
     ):
         if not self.use_cache:
             if progress_callback:
@@ -333,14 +335,19 @@ def checkout(
                 )
             return None
 
-        return self.cache.checkout(
-            self.path_info,
-            self.hash_info,
-            force=force,
-            progress_callback=progress_callback,
-            relink=relink,
-            filter_info=filter_info,
-        )
+        try:
+            return self.cache.checkout(
+                self.path_info,
+                self.hash_info,
+                force=force,
+                progress_callback=progress_callback,
+                relink=relink,
+                filter_info=filter_info,
+            )
+        except CheckoutError:
+            if self.persist and allow_persist_missing:
+                return None
+            raise
 
     def remove(self, ignore_remove=False):
         self.tree.remove(self.path_info)
diff --git a/dvc/repo/checkout.py b/dvc/repo/checkout.py
--- a/dvc/repo/checkout.py
+++ b/dvc/repo/checkout.py
@@ -46,6 +46,7 @@ def checkout(
     force=False,
     relink=False,
     recursive=False,
+    allow_persist_missing=False,
 ):
     from dvc.stage.exceptions import (
         StageFileBadNameError,
@@ -96,6 +97,7 @@ def checkout(
                 progress_callback=pbar.update_msg,
                 relink=relink,
                 filter_info=filter_info,
+                allow_persist_missing=allow_persist_missing,
             )
             for key, items in result.items():
                 stats[key].extend(_fspath_dir(path) for path in items)
diff --git a/dvc/repo/experiments/__init__.py b/dvc/repo/experiments/__init__.py
--- a/dvc/repo/experiments/__init__.py
+++ b/dvc/repo/experiments/__init__.py
@@ -79,7 +79,8 @@ class Experiments:
         r"dvc-exp:(?P<baseline_rev>[0-9a-f]+)(:(?P<branch>.+))?$"
     )
     BRANCH_RE = re.compile(
-        r"^(?P<baseline_rev>[a-f0-9]{7})-(?P<exp_sha>[a-f0-9]+)$"
+        r"^(?P<baseline_rev>[a-f0-9]{7})-(?P<exp_sha>[a-f0-9]+)"
+        r"(?P<checkpoint>-checkpoint)?$"
     )
 
     StashEntry = namedtuple("StashEntry", ["index", "baseline_rev", "branch"])
@@ -302,13 +303,16 @@ def _update(dict_, other):
             with modify_data(path, tree=self.exp_dvc.tree) as data:
                 _update(data, params[params_fname])
 
-    def _commit(self, exp_hash, check_exists=True, create_branch=True):
+    def _commit(
+        self, exp_hash, check_exists=True, create_branch=True, checkpoint=False
+    ):
         """Commit stages as an experiment and return the commit SHA."""
         if not self.scm.is_dirty():
             raise UnchangedExperimentError(self.scm.get_rev())
 
         rev = self.scm.get_rev()
-        exp_name = f"{rev[:7]}-{exp_hash}"
+        checkpoint = "-checkpoint" if checkpoint else ""
+        exp_name = f"{rev[:7]}-{exp_hash}{checkpoint}"
         if create_branch:
             if check_exists and exp_name in self.scm.list_branches():
                 logger.debug("Using existing experiment branch '%s'", exp_name)
@@ -323,13 +327,16 @@ def _commit(self, exp_hash, check_exists=True, create_branch=True):
 
     def reproduce_one(self, queue=False, **kwargs):
         """Reproduce and checkout a single experiment."""
+        checkpoint = kwargs.get("checkpoint", False)
         stash_rev = self.new(**kwargs)
         if queue:
             logger.info(
                 "Queued experiment '%s' for future execution.", stash_rev[:7]
             )
             return [stash_rev]
-        results = self.reproduce([stash_rev], keep_stash=False)
+        results = self.reproduce(
+            [stash_rev], keep_stash=False, checkpoint=checkpoint
+        )
         exp_rev = first(results)
         if exp_rev is not None:
             self.checkout_exp(exp_rev)
@@ -348,13 +355,31 @@ def reproduce_queued(self, **kwargs):
         return results
 
     @scm_locked
-    def new(self, *args, **kwargs):
+    def new(
+        self,
+        *args,
+        checkpoint: Optional[bool] = False,
+        checkpoint_continue: Optional[str] = None,
+        branch: Optional[str] = None,
+        **kwargs,
+    ):
         """Create a new experiment.
 
         Experiment will be reproduced and checked out into the user's
         workspace.
         """
-        branch = kwargs.get("branch")
+        if checkpoint_continue:
+            branch = self._get_branch_containing(checkpoint_continue)
+            if not branch:
+                raise DvcException(
+                    "Could not find checkpoint experiment "
+                    f"'{checkpoint_continue}'"
+                )
+            logger.debug(
+                "Continuing checkpoint experiment '%s'", checkpoint_continue
+            )
+            kwargs["apply_workspace"] = False
+
         if branch:
             rev = self.scm.resolve_rev(branch)
             logger.debug(
@@ -363,8 +388,11 @@ def new(self, *args, **kwargs):
         else:
             rev = self.repo.scm.get_rev()
         self._scm_checkout(rev)
+
         try:
-            stash_rev = self._stash_exp(*args, **kwargs)
+            stash_rev = self._stash_exp(
+                *args, branch=branch, allow_unchanged=checkpoint, **kwargs
+            )
         except UnchangedExperimentError as exc:
             logger.info("Reproducing existing experiment '%s'.", rev[:7])
             raise exc
@@ -378,6 +406,7 @@ def reproduce(
         self,
         revs: Optional[Iterable] = None,
         keep_stash: Optional[bool] = True,
+        checkpoint: Optional[bool] = False,
         **kwargs,
     ):
         """Reproduce the specified experiments.
@@ -428,7 +457,10 @@ def reproduce(
             self._collect_input(executor)
             executors[rev] = executor
 
-        exec_results = self._reproduce(executors, **kwargs)
+        if checkpoint:
+            exec_results = self._reproduce_checkpoint(executors)
+        else:
+            exec_results = self._reproduce(executors, **kwargs)
 
         if keep_stash:
             # only drop successfully run stashed experiments
@@ -480,30 +512,10 @@ def _reproduce(self, executors: dict, jobs: Optional[int] = 1) -> dict:
                         self._scm_checkout(executor.branch)
                     else:
                         self._scm_checkout(executor.baseline_rev)
-                    try:
-                        self._collect_output(executor)
-                    except DownloadError:
-                        logger.error(
-                            "Failed to collect output for experiment '%s'",
-                            rev,
-                        )
-                        continue
-                    finally:
-                        if os.path.exists(self.args_file):
-                            remove(self.args_file)
-
-                    try:
-                        branch = not executor.branch
-                        exp_rev = self._commit(exp_hash, create_branch=branch)
-                    except UnchangedExperimentError:
-                        logger.debug(
-                            "Experiment '%s' identical to baseline '%s'",
-                            rev,
-                            executor.baseline_rev,
-                        )
-                        exp_rev = executor.baseline_rev
-                    logger.info("Reproduced experiment '%s'.", exp_rev[:7])
-                    result[rev] = {exp_rev: exp_hash}
+                    exp_rev = self._collect_and_commit(rev, executor, exp_hash)
+                    if exp_rev:
+                        logger.info("Reproduced experiment '%s'.", exp_rev[:7])
+                        result[rev] = {exp_rev: exp_hash}
                 else:
                     logger.exception(
                         "Failed to reproduce experiment '%s'", rev
@@ -512,6 +524,76 @@ def _reproduce(self, executors: dict, jobs: Optional[int] = 1) -> dict:
 
         return result
 
+    def _reproduce_checkpoint(self, executors):
+        result = {}
+        for rev, executor in executors.items():
+            logger.debug("Reproducing checkpoint experiment '%s'", rev[:7])
+
+            if executor.branch:
+                self._scm_checkout(executor.branch)
+            else:
+                self._scm_checkout(executor.baseline_rev)
+
+            def _checkpoint_callback(rev, executor, unchanged, stages):
+                exp_hash = hash_exp(stages + unchanged)
+                exp_rev = self._collect_and_commit(
+                    rev, executor, exp_hash, checkpoint=True
+                )
+                if exp_rev:
+                    if not executor.branch:
+                        branch = self._get_branch_containing(exp_rev)
+                        executor.branch = branch
+                    logger.info(
+                        "Checkpoint experiment iteration '%s'.", exp_rev[:7]
+                    )
+                    result[rev] = {exp_rev: exp_hash}
+
+            checkpoint_func = partial(_checkpoint_callback, rev, executor)
+            executor.reproduce(
+                executor.dvc_dir,
+                cwd=executor.dvc.root_dir,
+                checkpoint=True,
+                checkpoint_func=checkpoint_func,
+                **executor.repro_kwargs,
+            )
+
+            # TODO: determine whether or not we should create a final
+            # checkpoint commit after repro is killed, or if we should only do
+            # it on explicit make_checkpoint() signals.
+
+        # NOTE: our cached GitPython Repo instance cannot be re-used if the
+        # checkpoint run was interrupted via SIGINT, so we need this hack
+        # to create a new git repo instance after checkpoint runs.
+        del self.scm
+
+        return result
+
+    def _collect_and_commit(self, rev, executor, exp_hash, **kwargs):
+        try:
+            self._collect_output(executor)
+        except DownloadError:
+            logger.error(
+                "Failed to collect output for experiment '%s'", rev,
+            )
+            return None
+        finally:
+            if os.path.exists(self.args_file):
+                remove(self.args_file)
+
+        try:
+            create_branch = not executor.branch
+            exp_rev = self._commit(
+                exp_hash, create_branch=create_branch, **kwargs
+            )
+        except UnchangedExperimentError:
+            logger.debug(
+                "Experiment '%s' identical to baseline '%s'",
+                rev,
+                executor.baseline_rev,
+            )
+            exp_rev = executor.baseline_rev
+        return exp_rev
+
     def _collect_input(self, executor: ExperimentExecutor):
         """Copy (upload) input from the experiments workspace to the executor
         tree.
@@ -674,6 +756,8 @@ def _get_branch_containing(self, rev):
             self._checkout_default_branch()
         try:
             name = self.scm.repo.git.branch(contains=rev)
+            if name.startswith("*"):
+                name = name[1:]
             return name.rsplit("/")[-1].strip()
         except GitCommandError:
             pass
diff --git a/dvc/repo/experiments/executor.py b/dvc/repo/experiments/executor.py
--- a/dvc/repo/experiments/executor.py
+++ b/dvc/repo/experiments/executor.py
@@ -134,9 +134,10 @@ def reproduce(dvc_dir, cwd=None, **kwargs):
 
         unchanged = []
 
-        def filter_pipeline(stage):
-            if isinstance(stage, PipelineStage):
-                unchanged.append(stage)
+        def filter_pipeline(stages):
+            unchanged.extend(
+                [stage for stage in stages if isinstance(stage, PipelineStage)]
+            )
 
         if cwd:
             old_cwd = os.getcwd()
@@ -148,7 +149,20 @@ def filter_pipeline(stage):
         try:
             logger.debug("Running repro in '%s'", cwd)
             dvc = Repo(dvc_dir)
-            dvc.checkout()
+
+            # NOTE: for checkpoint experiments we handle persist outs slightly
+            # differently than normal:
+            #
+            # - checkpoint out may not yet exist if this is the first time this
+            #   experiment has been run, this is not an error condition for
+            #   experiments
+            # - at the start of a repro run, we need to remove the persist out
+            #   and restore it to its last known (committed) state (which may
+            #   be removed/does not yet exist) so that our executor workspace
+            #   is not polluted with the (persistent) out from an unrelated
+            #   experiment run
+            checkpoint = kwargs.pop("checkpoint", False)
+            dvc.checkout(allow_persist_missing=checkpoint, force=checkpoint)
             stages = dvc.reproduce(on_unchanged=filter_pipeline, **kwargs)
         finally:
             if old_cwd is not None:
diff --git a/dvc/repo/experiments/show.py b/dvc/repo/experiments/show.py
--- a/dvc/repo/experiments/show.py
+++ b/dvc/repo/experiments/show.py
@@ -1,6 +1,9 @@
 import logging
 from collections import OrderedDict, defaultdict
 from datetime import datetime
+from typing import Optional
+
+from funcy import first
 
 from dvc.repo import locked
 from dvc.repo.metrics.show import _collect_metrics, _read_metrics
@@ -9,11 +12,11 @@
 logger = logging.getLogger(__name__)
 
 
-def _collect_experiment(repo, branch, stash=False, sha_only=True):
+def _collect_experiment(repo, rev, stash=False, sha_only=True):
     from git.exc import GitCommandError
 
     res = defaultdict(dict)
-    for rev in repo.brancher(revs=[branch]):
+    for rev in repo.brancher(revs=[rev]):
         if rev == "workspace":
             res["timestamp"] = None
         else:
@@ -53,6 +56,29 @@ def _resolve_commit(repo, rev):
     return commit
 
 
+def _collect_checkpoint_experiment(repo, branch, baseline, **kwargs):
+    res = OrderedDict()
+    exp_rev = repo.scm.resolve_rev(branch)
+    for rev in _branch_revs(repo, exp_rev, baseline):
+        res[rev] = _collect_experiment(repo, rev, **kwargs)
+        res[rev]["checkpoint_tip"] = exp_rev
+    return res
+
+
+def _branch_revs(repo, branch_tip, baseline: Optional[str] = None):
+    """Iterate over revisions in a given branch (from newest to oldest).
+
+    If baseline is set, iterator will stop when the specified revision is
+    reached.
+    """
+    commit = _resolve_commit(repo, branch_tip)
+    while commit is not None:
+        yield commit.hexsha
+        commit = first(commit.parents)
+        if commit and commit.hexsha == baseline:
+            return
+
+
 @locked
 def show(
     repo,
@@ -89,12 +115,18 @@ def show(
         if m:
             rev = repo.scm.resolve_rev(m.group("baseline_rev"))
             if rev in revs:
-                exp_rev = repo.experiments.scm.resolve_rev(exp_branch)
                 with repo.experiments.chdir():
-                    experiment = _collect_experiment(
-                        repo.experiments.exp_dvc, exp_branch
-                    )
-                res[rev][exp_rev] = experiment
+                    if m.group("checkpoint"):
+                        checkpoint_exps = _collect_checkpoint_experiment(
+                            repo.experiments.exp_dvc, exp_branch, rev
+                        )
+                        res[rev].update(checkpoint_exps)
+                    else:
+                        exp_rev = repo.experiments.scm.resolve_rev(exp_branch)
+                        experiment = _collect_experiment(
+                            repo.experiments.exp_dvc, exp_branch
+                        )
+                        res[rev][exp_rev] = experiment
 
     # collect queued (not yet reproduced) experiments
     for stash_rev, entry in repo.experiments.stash_revs.items():
diff --git a/dvc/repo/reproduce.py b/dvc/repo/reproduce.py
--- a/dvc/repo/reproduce.py
+++ b/dvc/repo/reproduce.py
@@ -1,4 +1,5 @@
 import logging
+from functools import partial
 
 from dvc.exceptions import InvalidArgumentError, ReproductionError
 from dvc.repo.experiments import UnchangedExperimentError
@@ -11,6 +12,14 @@
 
 
 def _reproduce_stage(stage, **kwargs):
+    def _run_callback(repro_callback):
+        _dump_stage(stage)
+        repro_callback([stage])
+
+    checkpoint_func = kwargs.pop("checkpoint_func", None)
+    if checkpoint_func:
+        kwargs["checkpoint_func"] = partial(_run_callback, checkpoint_func)
+
     if stage.frozen and not stage.is_import:
         logger.warning(
             "{} is frozen. Its dependencies are"
@@ -22,14 +31,18 @@ def _reproduce_stage(stage, **kwargs):
         return []
 
     if not kwargs.get("dry", False):
-        from ..dvcfile import Dvcfile
-
-        dvcfile = Dvcfile(stage.repo, stage.path)
-        dvcfile.dump(stage, update_pipeline=False)
+        _dump_stage(stage)
 
     return [stage]
 
 
+def _dump_stage(stage):
+    from ..dvcfile import Dvcfile
+
+    dvcfile = Dvcfile(stage.repo, stage.path)
+    dvcfile.dump(stage, update_pipeline=False)
+
+
 def _get_active_graph(G):
     import networkx as nx
 
@@ -75,6 +88,8 @@ def reproduce(
     queue = kwargs.pop("queue", False)
     run_all = kwargs.pop("run_all", False)
     jobs = kwargs.pop("jobs", 1)
+    checkpoint = kwargs.pop("checkpoint", False)
+    checkpoint_continue = kwargs.pop("checkpoint_continue", None)
     if (experiment or run_all) and self.experiments:
         try:
             return _reproduce_experiments(
@@ -86,6 +101,8 @@ def reproduce(
                 queue=queue,
                 run_all=run_all,
                 jobs=jobs,
+                checkpoint=checkpoint,
+                checkpoint_continue=checkpoint_continue,
                 **kwargs,
             )
         except UnchangedExperimentError:
@@ -219,16 +236,25 @@ def _reproduce_stages(
 
     force_downstream = kwargs.pop("force_downstream", False)
     result = []
+    unchanged = []
     # `ret` is used to add a cosmetic newline.
     ret = []
     for stage in pipeline:
         if ret:
             logger.info("")
 
+        checkpoint_func = kwargs.pop("checkpoint_func", None)
+        if checkpoint_func:
+            kwargs["checkpoint_func"] = partial(
+                _repro_callback, checkpoint_func, unchanged
+            )
+
         try:
             ret = _reproduce_stage(stage, **kwargs)
 
-            if len(ret) != 0 and force_downstream:
+            if len(ret) == 0:
+                unchanged.extend([stage])
+            elif force_downstream:
                 # NOTE: we are walking our pipeline from the top to the
                 # bottom. If one stage is changed, it will be reproduced,
                 # which tells us that we should force reproducing all of
@@ -238,9 +264,13 @@ def _reproduce_stages(
 
             if ret:
                 result.extend(ret)
-            elif on_unchanged is not None:
-                on_unchanged(stage)
         except Exception as exc:
             raise ReproductionError(stage.relpath) from exc
 
+    if on_unchanged is not None:
+        on_unchanged(unchanged)
     return result
+
+
+def _repro_callback(experiments_callback, unchanged, stages):
+    experiments_callback(unchanged, stages)
diff --git a/dvc/stage/decorators.py b/dvc/stage/decorators.py
--- a/dvc/stage/decorators.py
+++ b/dvc/stage/decorators.py
@@ -50,3 +50,19 @@ def wrapper(stage, *args, **kwargs):
         return ret
 
     return wrapper
+
+
+def relock_repo(f):
+    @wraps(f)
+    def wrapper(stage, *args, **kwargs):
+        stage.repo.lock.lock()
+        stage.repo.state.load()
+        try:
+            ret = f(stage, *args, **kwargs)
+        finally:
+            stage.repo.state.dump()
+            stage.repo.lock.unlock()
+            stage.repo._reset()  # pylint: disable=protected-access
+        return ret
+
+    return wrapper
diff --git a/dvc/stage/run.py b/dvc/stage/run.py
--- a/dvc/stage/run.py
+++ b/dvc/stage/run.py
@@ -3,15 +3,19 @@
 import signal
 import subprocess
 import threading
+from contextlib import contextmanager
 
 from dvc.utils import fix_env
 
-from .decorators import unlocked_repo
+from .decorators import relock_repo, unlocked_repo
 from .exceptions import StageCmdFailedError
 
 logger = logging.getLogger(__name__)
 
 
+CHECKPOINT_SIGNAL_FILE = "DVC_CHECKPOINT"
+
+
 def _nix_cmd(executable, cmd):
     opts = {"zsh": ["--no-rcs"], "bash": ["--noprofile", "--norc"]}
     name = os.path.basename(executable).lower()
@@ -35,8 +39,11 @@ def warn_if_fish(executable):
 
 
 @unlocked_repo
-def cmd_run(stage, *args, **kwargs):
+def cmd_run(stage, *args, checkpoint=False, **kwargs):
     kwargs = {"cwd": stage.wdir, "env": fix_env(None), "close_fds": True}
+    if checkpoint:
+        # indicate that checkpoint cmd is being run inside DVC
+        kwargs["env"].update({"DVC_CHECKPOINT": "1"})
 
     if os.name == "nt":
         kwargs["shell"] = True
@@ -81,8 +88,8 @@ def cmd_run(stage, *args, **kwargs):
         raise StageCmdFailedError(stage.cmd, retcode)
 
 
-def run_stage(stage, dry=False, force=False, **kwargs):
-    if not (dry or force):
+def run_stage(stage, dry=False, force=False, checkpoint_func=None, **kwargs):
+    if not (dry or force or checkpoint_func):
         from .cache import RunCacheNotFoundError
 
         try:
@@ -99,4 +106,59 @@ def run_stage(stage, dry=False, force=False, **kwargs):
     )
     logger.info("\t%s", stage.cmd)
     if not dry:
-        cmd_run(stage)
+        with checkpoint_monitor(stage, checkpoint_func) as monitor:
+            cmd_run(stage, checkpoint=monitor is not None)
+
+
+class CheckpointCond:
+    def __init__(self):
+        self.done = False
+        self.cond = threading.Condition()
+
+    def notify(self):
+        with self.cond:
+            self.done = True
+            self.cond.notify()
+
+    def wait(self, timeout=None):
+        with self.cond:
+            return self.cond.wait(timeout) or self.done
+
+
+@contextmanager
+def checkpoint_monitor(stage, callback_func):
+    if not callback_func:
+        yield None
+        return
+
+    done_cond = CheckpointCond()
+    monitor_thread = threading.Thread(
+        target=_checkpoint_run, args=(stage, callback_func, done_cond),
+    )
+
+    try:
+        monitor_thread.start()
+        yield monitor_thread
+    finally:
+        done_cond.notify()
+        monitor_thread.join()
+
+
+def _checkpoint_run(stage, callback_func, done_cond):
+    """Run callback_func whenever checkpoint signal file is present."""
+    signal_path = os.path.join(stage.repo.tmp_dir, CHECKPOINT_SIGNAL_FILE)
+    while True:
+        if os.path.exists(signal_path):
+            _run_callback(stage, callback_func)
+            logger.debug("Remove checkpoint signal file")
+            os.remove(signal_path)
+        if done_cond.wait(1):
+            return
+
+
+@relock_repo
+def _run_callback(stage, callback_func):
+    stage.save()
+    # TODO: do we need commit() (and check for --no-commit) here
+    logger.debug("Running checkpoint callback for stage '%s'", stage)
+    callback_func()

diff --git a/tests/func/experiments/test_experiments.py b/tests/func/experiments/test_experiments.py
--- a/tests/func/experiments/test_experiments.py
+++ b/tests/func/experiments/test_experiments.py
@@ -1,8 +1,47 @@
+from textwrap import dedent
+
 import pytest
+from funcy import first
 
 from dvc.utils.serialize import PythonFileCorruptedError
 from tests.func.test_repro_multistage import COPY_SCRIPT
 
+CHECKPOINT_SCRIPT_FORMAT = dedent(
+    """\
+    import os
+    import sys
+    import shutil
+    from time import sleep
+
+    from dvc.api import make_checkpoint
+
+    checkpoint_file = {}
+    checkpoint_iterations = int({})
+    if os.path.exists(checkpoint_file):
+        with open(checkpoint_file) as fobj:
+            try:
+                value = int(fobj.read())
+            except ValueError:
+                value = 0
+    else:
+        with open(checkpoint_file, "w"):
+            pass
+        value = 0
+
+    shutil.copyfile({}, {})
+
+    if os.getenv("DVC_CHECKPOINT"):
+        for _ in range(checkpoint_iterations):
+            value += 1
+            with open(checkpoint_file, "w") as fobj:
+                fobj.write(str(value))
+            make_checkpoint()
+"""
+)
+CHECKPOINT_SCRIPT = CHECKPOINT_SCRIPT_FORMAT.format(
+    "sys.argv[1]", "sys.argv[2]", "sys.argv[3]", "sys.argv[4]"
+)
+
 
 def test_new_simple(tmp_dir, scm, dvc, mocker):
     tmp_dir.gen("copy.py", COPY_SCRIPT)
@@ -236,3 +275,77 @@ def test_detached_parent(tmp_dir, scm, dvc, mocker):
     assert dvc.experiments.get_baseline(exp_rev) == detached_rev
     assert (tmp_dir / "params.yaml").read_text().strip() == "foo: 3"
     assert (tmp_dir / "metrics.yaml").read_text().strip() == "foo: 3"
+
+
+def test_new_checkpoint(tmp_dir, scm, dvc, mocker):
+    tmp_dir.gen("checkpoint.py", CHECKPOINT_SCRIPT)
+    tmp_dir.gen("params.yaml", "foo: 1")
+    stage = dvc.run(
+        cmd="python checkpoint.py foo 5 params.yaml metrics.yaml",
+        metrics_no_cache=["metrics.yaml"],
+        params=["foo"],
+        outs_persist=["foo"],
+        always_changed=True,
+        name="checkpoint-file",
+    )
+    scm.add(
+        [
+            "dvc.yaml",
+            "dvc.lock",
+            "checkpoint.py",
+            "params.yaml",
+            "metrics.yaml",
+        ]
+    )
+    scm.commit("init")
+
+    new_mock = mocker.spy(dvc.experiments, "new")
+    dvc.reproduce(
+        stage.addressing, experiment=True, checkpoint=True, params=["foo=2"]
+    )
+
+    new_mock.assert_called_once()
+    assert (tmp_dir / "foo").read_text() == "5"
+    assert (
+        tmp_dir / ".dvc" / "experiments" / "metrics.yaml"
+    ).read_text().strip() == "foo: 2"
+
+
+def test_continue_checkpoint(tmp_dir, scm, dvc, mocker):
+    tmp_dir.gen("checkpoint.py", CHECKPOINT_SCRIPT)
+    tmp_dir.gen("params.yaml", "foo: 1")
+    stage = dvc.run(
+        cmd="python checkpoint.py foo 5 params.yaml metrics.yaml",
+        metrics_no_cache=["metrics.yaml"],
+        params=["foo"],
+        outs_persist=["foo"],
+        always_changed=True,
+        name="checkpoint-file",
+    )
+    scm.add(
+        [
+            "dvc.yaml",
+            "dvc.lock",
+            "checkpoint.py",
+            "params.yaml",
+            "metrics.yaml",
+        ]
+    )
+    scm.commit("init")
+
+    results = dvc.reproduce(
+        stage.addressing, experiment=True, checkpoint=True, params=["foo=2"]
+    )
+    exp_rev = first(results)
+
+    dvc.reproduce(
+        stage.addressing,
+        experiment=True,
+        checkpoint=True,
+        checkpoint_continue=exp_rev,
+    )
+
+    assert (tmp_dir / "foo").read_text() == "10"
+    assert (
+        tmp_dir / ".dvc" / "experiments" / "metrics.yaml"
+    ).read_text().strip() == "foo: 2"
diff --git a/tests/func/test_repro.py b/tests/func/test_repro.py
--- a/tests/func/test_repro.py
+++ b/tests/func/test_repro.py
@@ -1302,4 +1302,4 @@ def test_repro_when_cmd_changes(tmp_dir, dvc, run_copy, mocker):
         stage.addressing: ["changed checksum"]
     }
     assert dvc.reproduce(stage.addressing)[0] == stage
-    m.assert_called_once_with(stage)
+    m.assert_called_once_with(stage, checkpoint=False)
diff --git a/tests/func/test_repro_multistage.py b/tests/func/test_repro_multistage.py
--- a/tests/func/test_repro_multistage.py
+++ b/tests/func/test_repro_multistage.py
@@ -286,7 +286,7 @@ def test_repro_when_cmd_changes(tmp_dir, dvc, run_copy, mocker):
 
     assert dvc.status([target]) == {target: ["changed command"]}
     assert dvc.reproduce(target)[0] == stage
-    m.assert_called_once_with(stage)
+    m.assert_called_once_with(stage, checkpoint=False)
 
 
 def test_repro_when_new_deps_is_added_in_dvcfile(tmp_dir, dvc, run_copy):
diff --git a/tests/func/test_stage.py b/tests/func/test_stage.py
--- a/tests/func/test_stage.py
+++ b/tests/func/test_stage.py
@@ -9,6 +9,7 @@
 from dvc.repo import Repo
 from dvc.stage import PipelineStage, Stage
 from dvc.stage.exceptions import StageFileFormatError
+from dvc.stage.run import run_stage
 from dvc.tree.local import LocalTree
 from dvc.utils.serialize import dump_yaml, load_yaml
 from tests.basic_env import TestDvc
@@ -274,3 +275,17 @@ def test_stage_remove_pointer_stage(tmp_dir, dvc, run_copy):
     with dvc.lock:
         stage.remove()
     assert not (tmp_dir / stage.relpath).exists()
+
+
+@pytest.mark.parametrize("checkpoint", [True, False])
+def test_stage_run_checkpoint(tmp_dir, dvc, mocker, checkpoint):
+    stage = Stage(dvc, "stage.dvc", cmd="mycmd arg1 arg2")
+    mocker.patch.object(stage, "save")
+
+    mock_cmd_run = mocker.patch("dvc.stage.run.cmd_run")
+    if checkpoint:
+        callback = mocker.Mock()
+    else:
+        callback = None
+    run_stage(stage, checkpoint_func=callback)
+    mock_cmd_run.assert_called_with(stage, checkpoint=checkpoint)
diff --git a/tests/unit/command/test_experiments.py b/tests/unit/command/test_experiments.py
--- a/tests/unit/command/test_experiments.py
+++ b/tests/unit/command/test_experiments.py
@@ -1,5 +1,10 @@
 from dvc.cli import parse_args
-from dvc.command.experiments import CmdExperimentsDiff, CmdExperimentsShow
+from dvc.command.experiments import (
+    CmdExperimentsDiff,
+    CmdExperimentsRun,
+    CmdExperimentsShow,
+)
+from dvc.dvcfile import PIPELINE_FILE
 
 
 def test_experiments_diff(dvc, mocker):
@@ -54,3 +59,34 @@ def test_experiments_show(dvc, mocker):
         all_commits=True,
         sha_only=True,
     )
+
+
+default_run_arguments = {
+    "all_pipelines": False,
+    "downstream": False,
+    "dry": False,
+    "force": False,
+    "run_cache": True,
+    "interactive": False,
+    "no_commit": False,
+    "pipeline": False,
+    "single_item": False,
+    "recursive": False,
+    "force_downstream": False,
+    "params": [],
+    "queue": False,
+    "run_all": False,
+    "jobs": None,
+    "checkpoint": False,
+    "checkpoint_continue": None,
+    "experiment": True,
+}
+
+
+def test_experiments_run(dvc, mocker):
+    cmd = CmdExperimentsRun(parse_args(["exp", "run"]))
+    mocker.patch.object(cmd.repo, "reproduce")
+    cmd.run()
+    cmd.repo.reproduce.assert_called_with(
+        PIPELINE_FILE, **default_run_arguments
+    )

Experiments: checkpoints tracking
# Checkpoints

The deep learning training process is very slow for complex neuro net models. Checkpoints are often used to track the progress of the training. Usually, a checkpoint is created for every N (1-100) epochs. For example, user's code can save models for every 10 epochs:
- `checkpoint/model_10.h5`
- `checkpoint/model_20.h5`
- `checkpoint/model_30.h5`
...
- `checkpoint/model_240.h5`

**Epoche** is the abstraction to index and name the checkpoints. Usually, code is not limited by max epoch and runs forever until the job won't be canceled (Ctrl+C or SIGTERM or `kill 1234`).

The checkpoints give to users many benefits:
1. **[Resume training]** Stop the training and resume it back later (might be in another machine).
2. **[Forward learning]** Training with a new hypothesis (set of parameters) starting from an old checkpoint. Stop training, change code, or hyper-params and restart it back using the last `checkpoint/model_240.h5`.
3. **[Backward learning]** Return back to a previous checkpoint If starts overfitting. Then resume the training with slightly different params (see 2).

So, the final model can be a result of many steps and combinations of 1-3 (and not reproducible).

# Problems

This process does not fit to DVC model for several reasons:
1. DVC is designed to work with a clean namespace and file versions. So, all the checkpoints should be just a version of the same file like `./model.h5`.
2. A checkpoint is a circular dependency. DVC has some support of that with `--outs-persist`.
3. DVC was not designed for jobs that run forever (until it will be killed form outside).

# Solution

## Checkpoint versions

New experiments #2799 can be a good abstraction for checkpoints and can solve problem 1 (checkpoint file versions). Example:

```
$ dvc exp show --no-pager
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━
┃ Experiment                         ┃ accuracy ┃    loss ┃ time_process ┃ epoch
┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━
│ workspace                          │  0.61124 │ 2.31573 │     2153.649 │  370
│ d1c200e (2020-08-27 11:18:07)      │  0.61124 │ 2.31573 │     2153.649 │  370
│ ├── 4310110 (2020-08-29 18:46:05)  │  0.13908 │ 2.32090 │       70.414 │   10
│ ├── c6133f2 (2020-08-29 18:51:53)  │  0.24523 │ 2.33397 │       71.864 │   20
│ ├── 2881848 (2020-08-29 18:56:29)  │  0.29831 │ 2.33397 │       71.942 │   30
│ └── 38a8f99 (2020-08-29 20:01:36)  │  0.35890 │ 2.05299 │       71.824 │   40
```

## Circular dependency

The circular dependency problem is partially solved in DVC by `--outs-persist` in `dvc run`.

## Infinite runs

We need to introduce a special type of job that can be canceled and the result still tracked as valid.
Also, `dvc repro` needs to understand that the job "type" is a checkpoint (or persist) and start training with a particular epoch.

This needs to be reflected properly in the experiments - the experiments has to be grouped somehow based on an initial commit. More interesting question - what to do for forward-learning (initial commit changed but epoch continue to growth) and backward-learning (return to a previous epoch, change it commit and continue to train).

# Other challenges and possible solutions

## Epoche tracking

How DVC knows how many epochs were executed in the users's code and which epoch is the starting one?

A possible solution -  epoch needs to be a parameter from `params.yaml` as well as metrics.

##  Data synchronization

How DVC knows that it is time to take a snapshot (save an experiment with the checksum, like `4310110` and `c6133f2` in the example)? Also, users' code needs to stop when DVC creates the experiment since this operation can take a lot of time (some models can be a few GB). So, a clear synchronization protocol needs to be established between DVC and user' code.

A possible solution - provide a library for users to signal DVC. This library can be based on dumping the metrics file (with epoch value) and locking the file. DVC can monitor the metrics file until it's unlocked. A backward connection is also needed. DVC can remove the file to signal it is done.

tests/func/test_stage.py::test_cmd_obj tests/func/test_stage.py::test_cmd_none tests/func/test_stage.py::test_no_cmd tests/func/test_stage.py::test_cmd_str tests/func/test_stage.py::test_object tests/func/test_stage.py::test_none tests/func/test_stage.py::test_empty_list tests/func/test_stage.py::test_list tests/func/test_stage.py::test_stage_on_no_path_string_repr tests/func/test_stage.py::test_stage_run_checkpoint[True] tests/func/test_stage.py::test_stage_run_checkpoint[False] tests/unit/command/test_experiments.py::test_experiments_diff tests/unit/command/test_experiments.py::test_experiments_show tests/unit/command/test_experiments.py::test_experiments_run