diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index b9fa806..466bc78 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -54,6 +54,7 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 - Added the ``run_sync_from_thread()`` function
 - Added ``UNIXSocketStream`` as a ``SocketStream`` subclass, capable of sending and receiving
   file descriptors
+- Added thread pooling for asyncio
 - Added the ``FileReadStream`` and ``FileWriteStream`` classes
 - Added the ``TaskGroup.start()`` method and a corresponding ``BlockingPortal.start_task()`` method
 - Added the ``name`` argument to ``BlockingPortal.spawn_task()``
@@ -81,6 +82,8 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 - Changed the asyncio ``TaskGroup.spawn()`` method to avoid the use of a coroutine wrapper on
   Python 3.8+ and added a hint for hiding the wrapper in tracebacks on earlier Pythons (supported
   by Pytest, Sentry etc.)
+- Changed the default thread limiter on asyncio to be scoped to an event loop so that multiple
+  running event loops don't conflict with each other
 
 **2.2.0**
 
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index ac67930..2ba1e8d 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -4,6 +4,7 @@ import concurrent.futures
 import math
 import socket
 import sys
+from asyncio.base_events import _run_until_complete_cb  # type: ignore
 from collections import OrderedDict, deque
 from concurrent.futures import Future
 from dataclasses import dataclass
@@ -11,8 +12,9 @@ from functools import partial, wraps
 from inspect import (
     CORO_RUNNING, CORO_SUSPENDED, GEN_RUNNING, GEN_SUSPENDED, getcoroutinestate, getgeneratorstate)
 from io import IOBase
+from queue import Empty, Queue
 from socket import AddressFamily, SocketKind, SocketType
-from threading import Thread
+from threading import Thread, current_thread
 from types import TracebackType
 from typing import (
     Any, Awaitable, Callable, Collection, Coroutine, Deque, Dict, Generator, List, Optional,
@@ -40,6 +42,15 @@ else:
 if sys.version_info >= (3, 7):
     from asyncio import all_tasks, create_task, current_task, get_running_loop
     from asyncio import run as native_run
+
+    def find_root_task() -> asyncio.Task:
+        for task in all_tasks():
+            if task._callbacks:
+                for cb, context in task._callbacks:  # type: ignore
+                    if cb is _run_until_complete_cb or cb.__module__ == 'uvloop.loop':
+                        return task
+
+        raise RuntimeError('Cannot find root task for setting cleanup callback')
 else:
 
     _T = TypeVar('_T')
@@ -115,6 +126,14 @@ else:
 
         return asyncio.Task.current_task(loop)
 
+    def find_root_task() -> asyncio.Task:
+        for task in all_tasks():
+            for cb in task._callbacks:
+                if cb is _run_until_complete_cb or cb.__module__ == 'uvloop.loop':
+                    return task
+
+        raise RuntimeError('Cannot find root task for setting cleanup callback')
+
 T_Retval = TypeVar('T_Retval')
 
 # Check whether there is native support for task names in asyncio (3.8+)
@@ -619,47 +638,87 @@ class TaskGroup(abc.TaskGroup):
 _Retval_Queue_Type = Tuple[Optional[T_Retval], Optional[BaseException]]
 
 
-async def run_sync_in_worker_thread(
-        func: Callable[..., T_Retval], *args, cancellable: bool = False,
-        limiter: Optional['CapacityLimiter'] = None) -> T_Retval:
-    def thread_worker():
+def _thread_pool_worker(work_queue: Queue, workers: Set[Thread],
+                        idle_workers: Set[Thread]) -> None:
+    func: Callable
+    args: tuple
+    future: asyncio.Future
+    limiter: CapacityLimiter
+    thread = current_thread()
+    while True:
         try:
+            func, args, future = work_queue.get(timeout=10)
+        except Empty:
+            workers.remove(thread)
+            return
+        finally:
+            idle_workers.discard(thread)
+
+        if func is None:
+            # Shutdown command received
+            workers.remove(thread)
+            return
+
+        if not future.cancelled():
             with claim_worker_thread('asyncio'):
-                threadlocals.loop = loop
-                result = func(*args)
-        except BaseException as exc:
-            if not loop.is_closed():
-                loop.call_soon_threadsafe(limiter.release_on_behalf_of, task)
-                if not cancelled:
-                    loop.call_soon_threadsafe(queue.put_nowait, (None, exc))
+                loop = threadlocals.loop = future._loop
+                try:
+                    result = func(*args)
+                except BaseException as exc:
+                    idle_workers.add(thread)
+                    if not loop.is_closed() and not future.cancelled():
+                        loop.call_soon_threadsafe(future.set_exception, exc)
+                else:
+                    idle_workers.add(thread)
+                    if not loop.is_closed() and not future.cancelled():
+                        loop.call_soon_threadsafe(future.set_result, result)
         else:
-            if not loop.is_closed():
-                loop.call_soon_threadsafe(limiter.release_on_behalf_of, task)
-                if not cancelled:
-                    loop.call_soon_threadsafe(queue.put_nowait, (result, None))
+            idle_workers.add(thread)
+
+        work_queue.task_done()
+
 
+_threadpool_work_queue: RunVar[Queue] = RunVar('_threadpool_work_queue')
+_threadpool_idle_workers: RunVar[Set[Thread]] = RunVar('_threadpool_idle_workers')
+_threadpool_workers: RunVar[Set[Thread]] = RunVar('_threadpool_workers')
+
+
+def _loop_shutdown_callback(f: asyncio.Future) -> None:
+    """This is called when the root task has finished."""
+    for _ in range(len(_threadpool_workers.get())):
+        _threadpool_work_queue.get().put_nowait((None, None, None))
+
+
+async def run_sync_in_worker_thread(
+        func: Callable[..., T_Retval], *args, cancellable: bool = False,
+        limiter: Optional['CapacityLimiter'] = None) -> T_Retval:
     await checkpoint()
-    loop = get_running_loop()
-    task = current_task()
-    queue: asyncio.Queue[_Retval_Queue_Type] = asyncio.Queue(1)
-    cancelled = False
-    limiter = limiter or _default_thread_limiter
-    await limiter.acquire_on_behalf_of(task)
-    thread = Thread(target=thread_worker, daemon=True)
-    thread.start()
-    exception: Optional[BaseException] = None
-    with CancelScope(shield=not cancellable):
-        try:
-            retval, exception = await queue.get()
-        except BaseException as exc:
-            exception = exc
-        finally:
-            cancelled = True
 
-    if exception is not None:
-        raise exception
-    else:
-        return cast(T_Retval, retval)
+    # If this is the first run in this event loop thread, set up the necessary variables
+    try:
+        work_queue = _threadpool_work_queue.get()
+        idle_workers = _threadpool_idle_workers.get()
+        workers = _threadpool_workers.get()
+    except LookupError:
+        work_queue = Queue()
+        idle_workers = set()
+        workers = set()
+        _threadpool_work_queue.set(work_queue)
+        _threadpool_idle_workers.set(idle_workers)
+        _threadpool_workers.set(workers)
+        find_root_task().add_done_callback(_loop_shutdown_callback)
+
+    async with (limiter or current_default_thread_limiter()):
+        with CancelScope(shield=not cancellable):
+            future: asyncio.Future = asyncio.Future()
+            work_queue.put_nowait((func, args, future))
+            if not idle_workers:
+                args = (work_queue, workers, idle_workers)
+                thread = Thread(target=_thread_pool_worker, args=args, name='AnyIO worker thread')
+                workers.add(thread)
+                thread.start()
+
+            return await future
 
 
 def run_sync_from_thread(func: Callable[..., T_Retval], *args,
@@ -1536,11 +1595,16 @@ class CapacityLimiter(abc.CapacityLimiter):
                                          tuple(self._borrowers), len(self._wait_queue))
 
 
-def current_default_thread_limiter():
-    return _default_thread_limiter
+_default_thread_limiter: RunVar[CapacityLimiter] = RunVar('_default_thread_limiter')
 
 
-_default_thread_limiter = CapacityLimiter(40)
+def current_default_thread_limiter():
+    try:
+        return _default_thread_limiter.get()
+    except LookupError:
+        limiter = CapacityLimiter(40)
+        _default_thread_limiter.set(limiter)
+        return limiter
 
 
 #

diff --git a/tests/test_threads.py b/tests/test_threads.py
index 9d07ed7..56eb5b8 100644
--- a/tests/test_threads.py
+++ b/tests/test_threads.py
@@ -9,7 +9,7 @@ import pytest
 
 from anyio import (
     create_blocking_portal, create_capacity_limiter, create_event, create_task_group,
-    get_cancelled_exc_class, get_current_task, run_async_from_thread, run_sync_from_thread,
+    get_cancelled_exc_class, get_current_task, run, run_async_from_thread, run_sync_from_thread,
     run_sync_in_worker_thread, sleep, start_blocking_portal, wait_all_tasks_blocked)
 
 if sys.version_info < (3, 7):
@@ -48,6 +48,23 @@ async def test_run_sync_from_thread():
     assert result == 3
 
 
+def test_run_sync_from_thread_pooling():
+    async def main():
+        thread_ids = set()
+        for _ in range(5):
+            thread_ids.add(await run_sync_in_worker_thread(threading.get_ident))
+
+        # Expects that all the work has been done in the same worker thread
+        assert len(thread_ids) == 1
+        assert thread_ids.pop() != threading.get_ident()
+        assert threading.active_count() == initial_count + 1
+
+    # The thread should not exist after the event loop has been closed
+    initial_count = threading.active_count()
+    run(main, backend='asyncio')
+    assert threading.active_count() == initial_count
+
+
 async def test_run_async_from_thread_exception():
     async def add(a, b):
         assert threading.get_ident() == event_loop_thread_id

Use thread pools in run_sync_in_worker_thread()
Right now, the asyncio implementation of this starts a new thread every time this function is called. We should be using thread pools instead, like trio does.
tests/test_threads.py::test_run_sync_from_thread_pooling
tests/test_threads.py::test_run_async_from_thread[asyncio] tests/test_threads.py::test_run_async_from_thread[asyncio+uvloop] tests/test_threads.py::test_run_sync_from_thread[asyncio] tests/test_threads.py::test_run_sync_from_thread[asyncio+uvloop] tests/test_threads.py::test_run_async_from_thread_exception[asyncio] tests/test_threads.py::test_run_async_from_thread_exception[asyncio+uvloop] tests/test_threads.py::test_run_sync_from_thread_exception[asyncio] tests/test_threads.py::test_run_sync_from_thread_exception[asyncio+uvloop] tests/test_threads.py::test_run_anyio_async_func_from_thread[asyncio] tests/test_threads.py::test_run_anyio_async_func_from_thread[asyncio+uvloop] tests/test_threads.py::test_run_in_thread_cancelled[asyncio] tests/test_threads.py::test_run_in_thread_cancelled[asyncio+uvloop] tests/test_threads.py::test_run_in_thread_exception[asyncio] tests/test_threads.py::test_run_in_thread_exception[asyncio+uvloop] tests/test_threads.py::test_run_in_custom_limiter[asyncio] tests/test_threads.py::test_run_in_custom_limiter[asyncio+uvloop] tests/test_threads.py::test_run_async_from_unclaimed_thread tests/test_threads.py::test_run_sync_from_unclaimed_thread tests/test_threads.py::test_cancel_worker_thread[asyncio-uncancellable] tests/test_threads.py::test_cancel_worker_thread[asyncio-cancellable] tests/test_threads.py::test_cancel_worker_thread[asyncio+uvloop-uncancellable] tests/test_threads.py::test_cancel_worker_thread[asyncio+uvloop-cancellable] tests/test_threads.py::test_cancel_asyncio_native_task[asyncio] tests/test_threads.py::TestBlockingPortal::test_successful_call[asyncio] tests/test_threads.py::TestBlockingPortal::test_successful_call[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_aexit_with_exception[asyncio] tests/test_threads.py::TestBlockingPortal::test_aexit_with_exception[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_aexit_without_exception[asyncio] tests/test_threads.py::TestBlockingPortal::test_aexit_without_exception[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_call_portal_from_event_loop_thread[asyncio] tests/test_threads.py::TestBlockingPortal::test_call_portal_from_event_loop_thread[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_with_new_event_loop[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_with_new_event_loop[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_with_nonexistent_backend tests/test_threads.py::TestBlockingPortal::test_call_stopped_portal[asyncio] tests/test_threads.py::TestBlockingPortal::test_call_stopped_portal[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_spawn_task[asyncio] tests/test_threads.py::TestBlockingPortal::test_spawn_task[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_spawn_task_cancel_later[asyncio] tests/test_threads.py::TestBlockingPortal::test_spawn_task_cancel_later[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_spawn_task_cancel_immediately[asyncio] tests/test_threads.py::TestBlockingPortal::test_spawn_task_cancel_immediately[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_spawn_task_with_name[asyncio] tests/test_threads.py::TestBlockingPortal::test_spawn_task_with_name[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_success[asyncio] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_success[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_error[asyncio] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_error[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_error_ignore[asyncio] tests/test_threads.py::TestBlockingPortal::test_async_context_manager_error_ignore[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_no_value[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_no_value[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_with_value[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_with_value[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_crash_before_started_call[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_crash_before_started_call[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_crash_after_started_call[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_crash_after_started_call[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_no_started_call[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_no_started_call[asyncio+uvloop] tests/test_threads.py::TestBlockingPortal::test_start_with_name[asyncio] tests/test_threads.py::TestBlockingPortal::test_start_with_name[asyncio+uvloop]