diff --git a/dvc/logger.py b/dvc/logger.py
--- a/dvc/logger.py
+++ b/dvc/logger.py
@@ -59,12 +59,28 @@ class ColorFormatter(logging.Formatter):
     def format(self, record):
         msg = record.msg.format(*record.args) if record.args else record.msg
         exception, stack_trace = self._parse_exc(record)
-        return ("{prefix}{description}{stack_trace}").format(
+        return ("{asctime}{prefix}{description}{stack_trace}").format(
+            asctime=self.formatTime(record, self.datefmt),
             prefix=self._prefix(record),
             description=self._description(msg, exception),
             stack_trace=stack_trace,
         )
 
+    def formatTime(self, record, datefmt=None):
+        # only show if current level is set to DEBUG
+        # also, skip INFO as it is used for UI
+        if (
+            self._current_level() != logging.DEBUG
+            or record.levelno == logging.INFO
+        ):
+            return ""
+
+        return "{color}{date}{nc} ".format(
+            color=colorama.Fore.GREEN,
+            date=super().formatTime(record, datefmt),
+            nc=colorama.Fore.RESET,
+        )
+
     def _prefix(self, record):
         if record.levelname == "INFO":
             return ""

Note: let's make timestamps show at the beginning of the message, in a human-readable format.
diff --git a/tests/unit/test_logger.py b/tests/unit/test_logger.py
--- a/tests/unit/test_logger.py
+++ b/tests/unit/test_logger.py
@@ -4,6 +4,10 @@
 import colorama
 
 import dvc.logger
+import time
+from datetime import datetime
+import pytest
+
 from dvc.exceptions import DvcException
 
 
@@ -11,18 +15,29 @@
 formatter = dvc.logger.ColorFormatter()
 colors = {
     "blue": colorama.Fore.BLUE,
+    "green": colorama.Fore.GREEN,
     "red": colorama.Fore.RED,
     "yellow": colorama.Fore.YELLOW,
     "nc": colorama.Fore.RESET,
 }
 
 
+@pytest.fixture()
+def dt(mocker):
+    with mocker.patch(
+        "time.time", return_value=time.mktime(datetime(2020, 2, 2).timetuple())
+    ):
+        yield "2020-02-02 00:00:00,000"
+
+
 class TestColorFormatter:
-    def test_debug(self, caplog):
+    def test_debug(self, caplog, dt):
         with caplog.at_level(logging.DEBUG, logger="dvc"):
             logger.debug("message")
 
-            expected = "{blue}DEBUG{nc}: message".format(**colors)
+            expected = "{green}{datetime}{nc} {blue}DEBUG{nc}: message".format(
+                **colors, datetime=dt
+            )
 
             assert expected == formatter.format(caplog.records[0])
 
@@ -81,7 +96,7 @@ def test_exception_with_description_and_message(self, caplog):
 
             assert expected == formatter.format(caplog.records[0])
 
-    def test_exception_under_verbose(self, caplog):
+    def test_exception_under_verbose(self, caplog, dt):
         with caplog.at_level(logging.DEBUG, logger="dvc"):
             try:
                 raise Exception("description")
@@ -90,17 +105,21 @@ def test_exception_under_verbose(self, caplog):
                 logger.exception("")
 
             expected = (
+                "{green}{datetime}{nc} "
                 "{red}ERROR{nc}: description\n"
                 "{red}{line}{nc}\n"
                 "{stack_trace}"
                 "{red}{line}{nc}".format(
-                    line="-" * 60, stack_trace=stack_trace, **colors
+                    line="-" * 60,
+                    stack_trace=stack_trace,
+                    **colors,
+                    datetime=dt
                 )
             )
 
             assert expected == formatter.format(caplog.records[0])
 
-    def test_tb_only(self, caplog):
+    def test_tb_only(self, caplog, dt):
         with caplog.at_level(logging.DEBUG, logger="dvc"):
             try:
                 raise Exception("description")
@@ -109,17 +128,21 @@ def test_tb_only(self, caplog):
                 logger.exception("something", extra={"tb_only": True})
 
             expected = (
+                "{green}{datetime}{nc} "
                 "{red}ERROR{nc}: something\n"
                 "{red}{line}{nc}\n"
                 "{stack_trace}"
                 "{red}{line}{nc}".format(
-                    line="-" * 60, stack_trace=stack_trace, **colors
+                    line="-" * 60,
+                    stack_trace=stack_trace,
+                    **colors,
+                    datetime=dt
                 )
             )
 
             assert expected == formatter.format(caplog.records[0])
 
-    def test_nested_exceptions(self, caplog):
+    def test_nested_exceptions(self, caplog, dt):
         with caplog.at_level(logging.DEBUG, logger="dvc"):
             try:
                 raise Exception("first")
@@ -131,11 +154,15 @@ def test_nested_exceptions(self, caplog):
                     logger.exception("message")
 
             expected = (
+                "{green}{datetime}{nc} "
                 "{red}ERROR{nc}: message - second: first\n"
                 "{red}{line}{nc}\n"
                 "{stack_trace}"
                 "{red}{line}{nc}".format(
-                    line="-" * 60, stack_trace=stack_trace, **colors
+                    line="-" * 60,
+                    stack_trace=stack_trace,
+                    **colors,
+                    datetime=dt
                 )
             )
             assert expected == formatter.format(caplog.records[0])
@@ -179,3 +206,21 @@ def test_handlers():
     assert out.level == logging.INFO
     assert deb.level == logging.DEBUG
     assert err.level == logging.WARNING
+
+
+def test_logging_debug_with_datetime(caplog, dt):
+    with caplog.at_level(logging.DEBUG, logger="dvc"):
+        logger.warning("WARNING")
+        logger.debug("DEBUG")
+        logger.error("ERROR")
+
+        for record in caplog.records:
+            assert dt in formatter.format(record)
+            assert record.levelname == record.message
+
+
+def test_info_with_debug_loglevel_shows_no_datetime(caplog, dt):
+    with caplog.at_level(logging.DEBUG, logger="dvc"):
+        logger.info("message")
+
+        assert "message" == formatter.format(caplog.records[0])

loggers: include timestamp to see how long operation takes
In logger output (mostly `dvc command -v`) we need to add time to see operation differences, see how long it took overall, etc. It's very valuable information.


tests/unit/test_logger.py::TestColorFormatter::test_debug tests/unit/test_logger.py::TestColorFormatter::test_exception_under_verbose tests/unit/test_logger.py::TestColorFormatter::test_tb_only tests/unit/test_logger.py::TestColorFormatter::test_nested_exceptions tests/unit/test_logger.py::test_logging_debug_with_datetime
tests/unit/test_logger.py::TestColorFormatter::test_info tests/unit/test_logger.py::TestColorFormatter::test_warning tests/unit/test_logger.py::TestColorFormatter::test_error tests/unit/test_logger.py::TestColorFormatter::test_exception tests/unit/test_logger.py::TestColorFormatter::test_exception_with_description_and_without_message tests/unit/test_logger.py::TestColorFormatter::test_exception_with_description_and_message tests/unit/test_logger.py::TestColorFormatter::test_progress_awareness tests/unit/test_logger.py::test_handlers tests/unit/test_logger.py::test_info_with_debug_loglevel_shows_no_datetime