diff --git a/asyncpg/pool.py b/asyncpg/pool.py
index e3898d53..2e4a7b4f 100644
--- a/asyncpg/pool.py
+++ b/asyncpg/pool.py
@@ -4,12 +4,16 @@
 # This module is part of asyncpg and is released under
 # the Apache 2.0 License: http://www.apache.org/licenses/LICENSE-2.0
 
+from __future__ import annotations
 
 import asyncio
+from collections.abc import Awaitable, Callable
 import functools
 import inspect
 import logging
 import time
+from types import TracebackType
+from typing import Any, Optional, Type
 import warnings
 
 from . import compat
@@ -23,7 +27,14 @@
 
 class PoolConnectionProxyMeta(type):
 
-    def __new__(mcls, name, bases, dct, *, wrap=False):
+    def __new__(
+        mcls,
+        name: str,
+        bases: tuple[Type[Any], ...],
+        dct: dict[str, Any],
+        *,
+        wrap: bool = False,
+    ) -> PoolConnectionProxyMeta:
         if wrap:
             for attrname in dir(connection.Connection):
                 if attrname.startswith('_') or attrname in dct:
@@ -44,8 +55,10 @@ def __new__(mcls, name, bases, dct, *, wrap=False):
         return super().__new__(mcls, name, bases, dct)
 
     @staticmethod
-    def _wrap_connection_method(meth_name, iscoroutine):
-        def call_con_method(self, *args, **kwargs):
+    def _wrap_connection_method(
+        meth_name: str, iscoroutine: bool
+    ) -> Callable[..., Any]:
+        def call_con_method(self: Any, *args: Any, **kwargs: Any) -> Any:
             # This method will be owned by PoolConnectionProxy class.
             if self._con is None:
                 raise exceptions.InterfaceError(
@@ -68,17 +81,18 @@ class PoolConnectionProxy(connection._ConnectionProxy,
 
     __slots__ = ('_con', '_holder')
 
-    def __init__(self, holder: 'PoolConnectionHolder',
-                 con: connection.Connection):
+    def __init__(
+        self, holder: PoolConnectionHolder, con: connection.Connection
+    ) -> None:
         self._con = con
         self._holder = holder
         con._set_proxy(self)
 
-    def __getattr__(self, attr):
+    def __getattr__(self, attr: str) -> Any:
         # Proxy all unresolved attributes to the wrapped Connection object.
         return getattr(self._con, attr)
 
-    def _detach(self) -> connection.Connection:
+    def _detach(self) -> Optional[connection.Connection]:
         if self._con is None:
             return
 
@@ -86,7 +100,7 @@ def _detach(self) -> connection.Connection:
         con._set_proxy(None)
         return con
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         if self._con is None:
             return '<{classname} [released] {id:#x}>'.format(
                 classname=self.__class__.__name__, id=id(self))
@@ -103,27 +117,34 @@ class PoolConnectionHolder:
                  '_inactive_callback', '_timeout',
                  '_generation')
 
-    def __init__(self, pool, *, max_queries, setup, max_inactive_time):
+    def __init__(
+        self,
+        pool: "Pool",
+        *,
+        max_queries: float,
+        setup: Optional[Callable[[PoolConnectionProxy], Awaitable[None]]],
+        max_inactive_time: float,
+    ) -> None:
 
         self._pool = pool
-        self._con = None
-        self._proxy = None
+        self._con: Optional[connection.Connection] = None
+        self._proxy: Optional[PoolConnectionProxy] = None
 
         self._max_queries = max_queries
         self._max_inactive_time = max_inactive_time
         self._setup = setup
-        self._inactive_callback = None
-        self._in_use = None  # type: asyncio.Future
-        self._timeout = None
-        self._generation = None
+        self._inactive_callback: Optional[Callable] = None
+        self._in_use: Optional[asyncio.Future] = None
+        self._timeout: Optional[float] = None
+        self._generation: Optional[int] = None
 
-    def is_connected(self):
+    def is_connected(self) -> bool:
         return self._con is not None and not self._con.is_closed()
 
-    def is_idle(self):
+    def is_idle(self) -> bool:
         return not self._in_use
 
-    async def connect(self):
+    async def connect(self) -> None:
         if self._con is not None:
             raise exceptions.InternalClientError(
                 'PoolConnectionHolder.connect() called while another '
@@ -171,7 +192,7 @@ async def acquire(self) -> PoolConnectionProxy:
 
         return proxy
 
-    async def release(self, timeout):
+    async def release(self, timeout: Optional[float]) -> None:
         if self._in_use is None:
             raise exceptions.InternalClientError(
                 'PoolConnectionHolder.release() called on '
@@ -234,25 +255,25 @@ async def release(self, timeout):
         # Rearm the connection inactivity timer.
         self._setup_inactive_callback()
 
-    async def wait_until_released(self):
+    async def wait_until_released(self) -> None:
         if self._in_use is None:
             return
         else:
             await self._in_use
 
-    async def close(self):
+    async def close(self) -> None:
         if self._con is not None:
             # Connection.close() will call _release_on_close() to
             # finish holder cleanup.
             await self._con.close()
 
-    def terminate(self):
+    def terminate(self) -> None:
         if self._con is not None:
             # Connection.terminate() will call _release_on_close() to
             # finish holder cleanup.
             self._con.terminate()
 
-    def _setup_inactive_callback(self):
+    def _setup_inactive_callback(self) -> None:
         if self._inactive_callback is not None:
             raise exceptions.InternalClientError(
                 'pool connection inactivity timer already exists')
@@ -261,12 +282,12 @@ def _setup_inactive_callback(self):
             self._inactive_callback = self._pool._loop.call_later(
                 self._max_inactive_time, self._deactivate_inactive_connection)
 
-    def _maybe_cancel_inactive_callback(self):
+    def _maybe_cancel_inactive_callback(self) -> None:
         if self._inactive_callback is not None:
             self._inactive_callback.cancel()
             self._inactive_callback = None
 
-    def _deactivate_inactive_connection(self):
+    def _deactivate_inactive_connection(self) -> None:
         if self._in_use is not None:
             raise exceptions.InternalClientError(
                 'attempting to deactivate an acquired connection')
@@ -280,12 +301,12 @@ def _deactivate_inactive_connection(self):
             # so terminate() above will not call the below.
             self._release_on_close()
 
-    def _release_on_close(self):
+    def _release_on_close(self) -> None:
         self._maybe_cancel_inactive_callback()
         self._release()
         self._con = None
 
-    def _release(self):
+    def _release(self) -> None:
         """Release this connection holder."""
         if self._in_use is None:
             # The holder is not checked out.
@@ -1012,7 +1033,7 @@ class PoolAcquireContext:
 
     __slots__ = ('timeout', 'connection', 'done', 'pool')
 
-    def __init__(self, pool, timeout):
+    def __init__(self, pool: Pool, timeout: Optional[float]) -> None:
         self.pool = pool
         self.timeout = timeout
         self.connection = None
@@ -1024,7 +1045,12 @@ async def __aenter__(self):
         self.connection = await self.pool._acquire(self.timeout)
         return self.connection
 
-    async def __aexit__(self, *exc):
+    async def __aexit__(
+        self,
+        exc_type: Optional[Type[BaseException]] = None,
+        exc_val: Optional[BaseException] = None,
+        exc_tb: Optional[TracebackType] = None,
+    ) -> None:
         self.done = True
         con = self.connection
         self.connection = None