diff --git a/asgiref/sync.py b/asgiref/sync.py
index 3710a7f1..435aa814 100644
--- a/asgiref/sync.py
+++ b/asgiref/sync.py
@@ -7,7 +7,9 @@
 import warnings
 import weakref
 from concurrent.futures import Future, ThreadPoolExecutor
-from typing import Any, Callable, Dict, Optional, overload
+from typing import Any, Awaitable, Callable, Dict, Optional, TypeVar, Union, overload
+
+from typing_extensions import ParamSpec
 
 from .compatibility import current_task, get_running_loop
 from .current_thread_executor import CurrentThreadExecutor
@@ -18,6 +20,9 @@
 else:
     contextvars = None
 
+P = ParamSpec("P")
+R = TypeVar("R")
+
 
 def _restore_context(context):
     # Check for changes in contextvars, and set them to the current
@@ -118,7 +123,9 @@ class AsyncToSync:
     # Local, not a threadlocal, so that tasks can work out what their parent used.
     executors = Local()
 
-    def __init__(self, awaitable, force_new_loop=False):
+    def __init__(
+        self, awaitable: Callable[..., Awaitable[Any]], force_new_loop: bool = False
+    ):
         if not callable(awaitable) or not _iscoroutinefunction_or_partial(awaitable):
             # Python does not have very reliable detection of async functions
             # (lots of false negatives) so this is just a warning.
@@ -127,7 +134,7 @@ def __init__(self, awaitable, force_new_loop=False):
             )
         self.awaitable = awaitable
         try:
-            self.__self__ = self.awaitable.__self__
+            self.__self__ = self.awaitable.__self__  # type: ignore
         except AttributeError:
             pass
         if force_new_loop:
@@ -507,8 +514,36 @@ def get_current_task():
             return None
 
 
-# Lowercase aliases (and decorator friendliness)
-async_to_sync = AsyncToSync
+# Lowercase aliases (and decorator/typing friendliness)
+@overload
+def async_to_sync(
+    func: None = None,
+    force_new_loop: bool = False,
+) -> Callable[[Callable[P, Awaitable[R]]], Callable[P, R]]:
+    ...
+
+
+@overload
+def async_to_sync(
+    func: Callable[P, Awaitable[R]],
+    force_new_loop: bool = False,
+) -> Callable[P, R]:
+    ...
+
+
+def async_to_sync(
+    func: Optional[Callable[P, Awaitable[R]]] = None,
+    force_new_loop: bool = False,
+) -> Union[Callable[P, R], Callable[[Callable[P, Awaitable[R]]], Callable[P, R]]]:
+    if func is None:
+        return lambda f: AsyncToSync(
+            f,
+            force_new_loop=force_new_loop,
+        )
+    return AsyncToSync(
+        func,
+        force_new_loop=force_new_loop,
+    )
 
 
 @overload
@@ -516,24 +551,26 @@ def sync_to_async(
     func: None = None,
     thread_sensitive: bool = True,
     executor: Optional["ThreadPoolExecutor"] = None,
-) -> Callable[[Callable[..., Any]], SyncToAsync]:
+) -> Callable[[Callable[P, R]], Callable[P, Awaitable[R]]]:
     ...
 
 
 @overload
 def sync_to_async(
-    func: Callable[..., Any],
+    func: Callable[P, R],
     thread_sensitive: bool = True,
     executor: Optional["ThreadPoolExecutor"] = None,
-) -> SyncToAsync:
+) -> Callable[P, Awaitable[R]]:
     ...
 
 
 def sync_to_async(
-    func=None,
-    thread_sensitive=True,
-    executor=None,
-):
+    func: Optional[Callable[P, R]] = None,
+    thread_sensitive: bool = True,
+    executor: Optional["ThreadPoolExecutor"] = None,
+) -> Union[
+    Callable[P, Awaitable[R]], Callable[[Callable[P, R]], Callable[P, Awaitable[R]]]
+]:
     if func is None:
         return lambda f: SyncToAsync(
             f,
diff --git a/setup.cfg b/setup.cfg
index 01d0b50b..62bd85c7 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -38,7 +38,7 @@ zip_safe = false
 tests =
     pytest
     pytest-asyncio
-    mypy>=0.800
+    mypy>=0.920
 
 [tool:pytest]
 testpaths = tests