diff --git a/CHANGES/5494.bugfix b/CHANGES/5494.bugfix
new file mode 100644
index 00000000000..20db5581f46
--- /dev/null
+++ b/CHANGES/5494.bugfix
@@ -0,0 +1,4 @@
+Fixed the multipart POST requests processing to always release file
+descriptors for the ``tempfile.Temporaryfile``-created
+``_io.BufferedRandom`` instances of files sent within multipart request
+bodies via HTTP POST requests -- by :user:`webknjaz`.
diff --git a/CHANGES/5494.misc b/CHANGES/5494.misc
new file mode 100644
index 00000000000..fc00335ff1f
--- /dev/null
+++ b/CHANGES/5494.misc
@@ -0,0 +1,3 @@
+Made sure to always close most of file descriptors and release other
+resouces in tests. Started ignoring ``ResourceWarning``s in pytest for
+warnings that are hard to track -- by :user:`webknjaz`.
diff --git a/aiohttp/web_request.py b/aiohttp/web_request.py
index d48a37461c9..ed5aae1adf4 100644
--- a/aiohttp/web_request.py
+++ b/aiohttp/web_request.py
@@ -720,6 +720,7 @@ async def post(self) -> "MultiDictProxy[Union[str, bytes, FileField]]":
                             tmp.write(chunk)
                             size += len(chunk)
                             if 0 < max_size < size:
+                                tmp.close()
                                 raise HTTPRequestEntityTooLarge(
                                     max_size=max_size, actual_size=size
                                 )
diff --git a/setup.cfg b/setup.cfg
index 55843384cf9..8e1fdfbbe04 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -54,6 +54,11 @@ addopts =
 filterwarnings =
     error
     ignore:module 'ssl' has no attribute 'OP_NO_COMPRESSION'. The Python interpreter is compiled against OpenSSL < 1.0.0. Ref. https.//docs.python.org/3/library/ssl.html#ssl.OP_NO_COMPRESSION:UserWarning
+    ignore:Exception ignored in. <function _SSLProtocolTransport.__del__ at.:pytest.PytestUnraisableExceptionWarning:_pytest.unraisableexception
+    ignore:Exception ignored in. <coroutine object BaseConnector.close at 0x.:pytest.PytestUnraisableExceptionWarning:_pytest.unraisableexception
+    ignore:Exception ignored in. <coroutine object ClientSession._request at 0x.:pytest.PytestUnraisableExceptionWarning:_pytest.unraisableexception
+    ignore:Exception ignored in. <function ClientSession.__del__ at 0x.:pytest.PytestUnraisableExceptionWarning:_pytest.unraisableexception
+    ignore:Exception ignored in. <_io.FileIO .closed.>:pytest.PytestUnraisableExceptionWarning:_pytest.unraisableexception
     # Temporarily ignore warnings internal to Python 3.9.7, can be removed again in 3.9.8.
     ignore:The loop argument is deprecated since Python 3.8, and scheduled for removal in Python 3.10.:DeprecationWarning:asyncio
 junit_suite_name = aiohttp_test_suite
diff --git a/tests/test_client_functional.py b/tests/test_client_functional.py
index b0750fa561e..36ef35bdf3b 100644
--- a/tests/test_client_functional.py
+++ b/tests/test_client_functional.py
@@ -2581,6 +2581,8 @@ async def handler(request):
     with pytest.raises(TypeError):
         await aiohttp.request("GET", server.make_url("/"))
 
+    server.close()
+
 
 async def test_yield_from_in_session_request(aiohttp_client) -> None:
     # a test for backward compatibility with yield from syntax
@@ -2770,7 +2772,7 @@ def connection_lost(self, exc):
         await r.read()
         assert 0 == len(connector._conns)
     await session.close()
-    connector.close()
+    await connector.close()
     server.close()
     await server.wait_closed()
 
@@ -2812,7 +2814,7 @@ def connection_lost(self, exc):
     assert 0 == len(connector._conns)
 
     await session.close()
-    connector.close()
+    await connector.close()
     server.close()
     await server.wait_closed()
 
diff --git a/tests/test_client_request.py b/tests/test_client_request.py
index 04ea8fa87e2..09136ad766a 100644
--- a/tests/test_client_request.py
+++ b/tests/test_client_request.py
@@ -279,6 +279,7 @@ def test_default_loop(loop) -> None:
     asyncio.set_event_loop(loop)
     req = ClientRequest("get", URL("http://python.org/"))
     assert req.loop is loop
+    loop.run_until_complete(req.close())
 
 
 def test_default_headers_useragent(make_request) -> None:
@@ -584,6 +585,8 @@ async def test_connection_header(loop, conn) -> None:
     await req.send(conn)
     assert req.headers.get("CONNECTION") == "close"
 
+    await req.close()
+
 
 async def test_no_content_length(loop, conn) -> None:
     req = ClientRequest("get", URL("http://python.org"), loop=loop)
@@ -606,6 +609,7 @@ async def test_content_type_auto_header_get(loop, conn) -> None:
     resp = await req.send(conn)
     assert "CONTENT-TYPE" not in req.headers
     resp.close()
+    await req.close()
 
 
 async def test_content_type_auto_header_form(loop, conn) -> None:
@@ -615,6 +619,7 @@ async def test_content_type_auto_header_form(loop, conn) -> None:
     resp = await req.send(conn)
     assert "application/x-www-form-urlencoded" == req.headers.get("CONTENT-TYPE")
     resp.close()
+    await req.close()
 
 
 async def test_content_type_auto_header_bytes(loop, conn) -> None:
@@ -622,6 +627,7 @@ async def test_content_type_auto_header_bytes(loop, conn) -> None:
     resp = await req.send(conn)
     assert "application/octet-stream" == req.headers.get("CONTENT-TYPE")
     resp.close()
+    await req.close()
 
 
 async def test_content_type_skip_auto_header_bytes(loop, conn) -> None:
@@ -635,6 +641,7 @@ async def test_content_type_skip_auto_header_bytes(loop, conn) -> None:
     resp = await req.send(conn)
     assert "CONTENT-TYPE" not in req.headers
     resp.close()
+    await req.close()
 
 
 async def test_content_type_skip_auto_header_form(loop, conn) -> None:
@@ -648,6 +655,7 @@ async def test_content_type_skip_auto_header_form(loop, conn) -> None:
     resp = await req.send(conn)
     assert "CONTENT-TYPE" not in req.headers
     resp.close()
+    await req.close()
 
 
 async def test_content_type_auto_header_content_length_no_skip(loop, conn) -> None:
@@ -661,6 +669,7 @@ async def test_content_type_auto_header_content_length_no_skip(loop, conn) -> No
     resp = await req.send(conn)
     assert req.headers.get("CONTENT-LENGTH") == "3"
     resp.close()
+    await req.close()
 
 
 async def test_urlencoded_formdata_charset(loop, conn) -> None:
@@ -674,6 +683,7 @@ async def test_urlencoded_formdata_charset(loop, conn) -> None:
     assert "application/x-www-form-urlencoded; charset=koi8-r" == req.headers.get(
         "CONTENT-TYPE"
     )
+    await req.close()
 
 
 async def test_post_data(loop, conn) -> None:
@@ -710,6 +720,7 @@ async def test_pass_falsy_data_file(loop, tmpdir) -> None:
     )
     assert req.headers.get("CONTENT-LENGTH", None) is not None
     await req.close()
+    testfile.close()
 
 
 # Elasticsearch API requires to send request body with GET-requests
@@ -908,6 +919,7 @@ async def test_expect100(loop, conn) -> None:
     assert req._continue is not None
     req.terminate()
     resp.close()
+    await req.close()
 
 
 async def test_expect_100_continue_header(loop, conn) -> None:
@@ -919,6 +931,7 @@ async def test_expect_100_continue_header(loop, conn) -> None:
     assert req._continue is not None
     req.terminate()
     resp.close()
+    await req.close()
 
 
 async def test_data_stream(loop, buf, conn) -> None:
@@ -1120,6 +1133,8 @@ async def test_oserror_on_write_bytes(loop, conn) -> None:
     exc = conn.protocol.set_exception.call_args[0][0]
     assert isinstance(exc, aiohttp.ClientOSError)
 
+    await req.close()
+
 
 async def test_terminate(loop, conn) -> None:
     req = ClientRequest("get", URL("http://python.org"), loop=loop)
@@ -1132,6 +1147,8 @@ async def test_terminate(loop, conn) -> None:
     writer.cancel.assert_called_with()
     resp.close()
 
+    await req.close()
+
 
 def test_terminate_with_closed_loop(loop, conn) -> None:
     req = resp = writer = None
@@ -1147,6 +1164,7 @@ async def go():
 
     loop.run_until_complete(go())
 
+    loop.run_until_complete(req.close())
     loop.close()
     req.terminate()
     assert req._writer is None
@@ -1161,6 +1179,8 @@ def test_terminate_without_writer(loop) -> None:
     req.terminate()
     assert req._writer is None
 
+    loop.run_until_complete(req.close())
+
 
 async def test_custom_req_rep(loop) -> None:
     conn = None
@@ -1259,3 +1279,5 @@ def test_loose_cookies_types(loop) -> None:
 
     for loose_cookies_type in accepted_types:
         req.update_cookies(cookies=loose_cookies_type)
+
+    loop.run_until_complete(req.close())
diff --git a/tests/test_client_response.py b/tests/test_client_response.py
index 1798c5b5d16..f8bee42be49 100644
--- a/tests/test_client_response.py
+++ b/tests/test_client_response.py
@@ -46,6 +46,7 @@ async def test_http_processing_error(session) -> None:
         await response.start(connection)
 
     assert info.value.request_info is request_info
+    response.close()
 
 
 def test_del(session) -> None:
diff --git a/tests/test_client_session.py b/tests/test_client_session.py
index 4e2824b21a6..02219816c96 100644
--- a/tests/test_client_session.py
+++ b/tests/test_client_session.py
@@ -30,7 +30,7 @@ async def make_conn():
     proto = mock.Mock()
     conn._conns["a"] = [(proto, 123)]
     yield conn
-    conn.close()
+    loop.run_until_complete(conn.close())
 
 
 @pytest.fixture
@@ -292,7 +292,7 @@ async def test_connector(create_session, loop, mocker) -> None:
 
     await session.close()
     assert connector.close.called
-    connector.close()
+    await connector.close()
 
 
 async def test_create_connector(create_session, loop, mocker) -> None:
@@ -314,7 +314,6 @@ async def make_connector():
 
         connector = another_loop.run_until_complete(make_connector())
 
-        stack.enter_context(contextlib.closing(connector))
         with pytest.raises(RuntimeError) as ctx:
 
             async def make_sess():
@@ -326,8 +325,11 @@ async def make_sess():
             == str(ctx.value).strip()
         )
 
+        # Cannot use `AsyncExitStack` as it's Python 3.7+:
+        another_loop.run_until_complete(connector.close())
 
-def test_detach(session) -> None:
+
+def test_detach(loop, session) -> None:
     conn = session.connector
     try:
         assert not conn.closed
@@ -336,7 +338,7 @@ def test_detach(session) -> None:
         assert session.closed
         assert not conn.closed
     finally:
-        conn.close()
+        loop.run_until_complete(conn.close())
 
 
 async def test_request_closed_session(session) -> None:
@@ -345,10 +347,10 @@ async def test_request_closed_session(session) -> None:
         await session.request("get", "/")
 
 
-def test_close_flag_for_closed_connector(session) -> None:
+def test_close_flag_for_closed_connector(loop, session) -> None:
     conn = session.connector
     assert not session.closed
-    conn.close()
+    loop.run_until_complete(conn.close())
     assert session.closed
 
 
@@ -514,6 +516,7 @@ async def handler(request):
 async def test_session_default_version(loop) -> None:
     session = aiohttp.ClientSession(loop=loop)
     assert session.version == aiohttp.HttpVersion11
+    await session.close()
 
 
 async def test_session_loop(loop) -> None:
@@ -639,6 +642,8 @@ async def test_request_tracing_exception() -> None:
         )
         assert not on_request_end.called
 
+    await session.close()
+
 
 async def test_request_tracing_interpose_headers(loop, aiohttp_client) -> None:
     async def handler(request):
@@ -681,6 +686,7 @@ async def test_client_session_custom_attr(loop) -> None:
     session = ClientSession(loop=loop)
     with pytest.warns(DeprecationWarning):
         session.custom = None
+    await session.close()
 
 
 async def test_client_session_timeout_args(loop) -> None:
@@ -701,15 +707,20 @@ async def test_client_session_timeout_args(loop) -> None:
             loop=loop, timeout=client.ClientTimeout(total=10 * 60), conn_timeout=30 * 60
         )
 
+    await session1.close()
+    await session2.close()
+
 
 async def test_client_session_timeout_default_args(loop) -> None:
     session1 = ClientSession()
     assert session1.timeout == client.DEFAULT_TIMEOUT
+    await session1.close()
 
 
 async def test_client_session_timeout_argument() -> None:
     session = ClientSession(timeout=500)
     assert session.timeout == 500
+    await session.close()
 
 
 async def test_client_session_timeout_zero() -> None:
@@ -724,11 +735,13 @@ async def test_client_session_timeout_zero() -> None:
 async def test_requote_redirect_url_default() -> None:
     session = ClientSession()
     assert session.requote_redirect_url
+    await session.close()
 
 
 async def test_requote_redirect_url_default_disable() -> None:
     session = ClientSession(requote_redirect_url=False)
     assert not session.requote_redirect_url
+    await session.close()
 
 
 async def test_requote_redirect_setter() -> None:
@@ -737,3 +750,4 @@ async def test_requote_redirect_setter() -> None:
     with pytest.warns(DeprecationWarning):
         session.requote_redirect_url = False
     assert not session.requote_redirect_url
+    await session.close()
diff --git a/tests/test_connector.py b/tests/test_connector.py
index 52dd83bbd68..74034dcceeb 100644
--- a/tests/test_connector.py
+++ b/tests/test_connector.py
@@ -273,7 +273,7 @@ async def test_close(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop)
     assert not conn.closed
     conn._conns[("host", 8080, False)] = [(proto, object())]
-    conn.close()
+    await conn.close()
 
     assert not conn._conns
     assert proto.close.called
@@ -287,7 +287,7 @@ async def test_get(loop) -> None:
     proto = mock.Mock()
     conn._conns[1] = [(proto, loop.time())]
     assert conn._get(1) == proto
-    conn.close()
+    await conn.close()
 
 
 async def test_get_unconnected_proto(loop) -> None:
@@ -331,7 +331,7 @@ async def test_get_expired(loop) -> None:
     conn._conns[key] = [(proto, loop.time() - 1000)]
     assert conn._get(key) is None
     assert not conn._conns
-    conn.close()
+    await conn.close()
 
 
 async def test_get_expired_ssl(loop) -> None:
@@ -345,7 +345,7 @@ async def test_get_expired_ssl(loop) -> None:
     assert conn._get(key) is None
     assert not conn._conns
     assert conn._cleanup_closed_transports == [transport]
-    conn.close()
+    await conn.close()
 
 
 async def test_release_acquired(loop, key) -> None:
@@ -364,7 +364,7 @@ async def test_release_acquired(loop, key) -> None:
     assert 0 == len(conn._acquired)
     assert 0 == len(conn._acquired_per_host)
 
-    conn.close()
+    await conn.close()
 
 
 async def test_release_acquired_closed(loop, key) -> None:
@@ -379,7 +379,7 @@ async def test_release_acquired_closed(loop, key) -> None:
     assert 1 == len(conn._acquired)
     assert 1 == len(conn._acquired_per_host[key])
     assert not conn._release_waiter.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release(loop, key) -> None:
@@ -397,7 +397,7 @@ async def test_release(loop, key) -> None:
     assert conn._conns[key][0][0] == proto
     assert conn._conns[key][0][1] == pytest.approx(loop.time(), abs=0.1)
     assert not conn._cleanup_closed_transports
-    conn.close()
+    await conn.close()
 
 
 async def test_release_ssl_transport(loop, ssl_key) -> None:
@@ -411,7 +411,7 @@ async def test_release_ssl_transport(loop, ssl_key) -> None:
 
     conn._release(ssl_key, proto, should_close=True)
     assert conn._cleanup_closed_transports == [transport]
-    conn.close()
+    await conn.close()
 
 
 async def test_release_already_closed(loop) -> None:
@@ -420,7 +420,7 @@ async def test_release_already_closed(loop) -> None:
     proto = mock.Mock()
     key = 1
     conn._acquired.add(proto)
-    conn.close()
+    await conn.close()
 
     conn._release_waiters = mock.Mock()
     conn._release_acquired = mock.Mock()
@@ -439,7 +439,7 @@ async def test_release_waiter_no_limit(loop, key, key2) -> None:
     conn._release_waiter()
     assert len(conn._waiters[key]) == 0
     assert w.done.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_waiter_first_available(loop, key, key2) -> None:
@@ -456,7 +456,7 @@ async def test_release_waiter_first_available(loop, key, key2) -> None:
         or not w1.set_result.called
         and w2.set_result.called
     )
-    conn.close()
+    await conn.close()
 
 
 async def test_release_waiter_release_first(loop, key, key2) -> None:
@@ -468,7 +468,7 @@ async def test_release_waiter_release_first(loop, key, key2) -> None:
     conn._release_waiter()
     assert w1.set_result.called
     assert not w2.set_result.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_waiter_skip_done_waiter(loop, key, key2) -> None:
@@ -480,7 +480,7 @@ async def test_release_waiter_skip_done_waiter(loop, key, key2) -> None:
     conn._release_waiter()
     assert not w1.set_result.called
     assert w2.set_result.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_waiter_per_host(loop, key, key2) -> None:
@@ -495,7 +495,7 @@ async def test_release_waiter_per_host(loop, key, key2) -> None:
     assert (w1.set_result.called and not w2.set_result.called) or (
         not w1.set_result.called and w2.set_result.called
     )
-    conn.close()
+    await conn.close()
 
 
 async def test_release_waiter_no_available(loop, key, key2) -> None:
@@ -508,7 +508,7 @@ async def test_release_waiter_no_available(loop, key, key2) -> None:
     conn._release_waiter()
     assert len(conn._waiters) == 1
     assert not w.done.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_close(loop, key) -> None:
@@ -661,7 +661,7 @@ def get_extra_info(param):
 
     conn._loop.create_connection = create_connection
 
-    await conn.connect(req, [], ClientTimeout())
+    established_connection = await conn.connect(req, [], ClientTimeout())
     assert ips == ips_tried
 
     assert os_error
@@ -670,6 +670,8 @@ def get_extra_info(param):
     assert fingerprint_error
     assert connected
 
+    established_connection.close()
+
 
 async def test_tcp_connector_resolve_host(loop) -> None:
     conn = aiohttp.TCPConnector(loop=loop, use_dns_cache=True)
@@ -765,7 +767,7 @@ async def test_tcp_connector_dns_throttle_requests_cancelled_when_close(
         f = loop.create_task(conn._resolve_host("localhost", 8080))
 
         await asyncio.sleep(0)
-        conn.close()
+        await conn.close()
 
         with pytest.raises(asyncio.CancelledError):
             await f
@@ -980,7 +982,7 @@ async def test_release_close_do_not_delete_existing_connections(key) -> None:
     conn._release(key, proto)
     assert conn._conns[key] == [(proto1, 1)]
     assert proto.close.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_not_started(loop) -> None:
@@ -994,7 +996,7 @@ async def test_release_not_started(loop) -> None:
     assert rec[0][0] == proto
     assert rec[0][1] == pytest.approx(loop.time(), abs=0.05)
     assert not proto.close.called
-    conn.close()
+    await conn.close()
 
 
 async def test_release_not_opened(loop, key) -> None:
@@ -1074,7 +1076,7 @@ async def test_close_during_connect(loop) -> None:
 
     task = loop.create_task(conn.connect(req, None, ClientTimeout()))
     await asyncio.sleep(0)
-    conn.close()
+    await conn.close()
 
     fut.set_result(proto)
     with pytest.raises(aiohttp.ClientConnectionError):
@@ -1143,7 +1145,7 @@ async def test_cleanup2() -> None:
 
     assert conn._cleanup_handle is not None
     loop.call_at.assert_called_with(310, mock.ANY, mock.ANY)
-    conn.close()
+    await conn.close()
 
 
 async def test_cleanup3(key) -> None:
@@ -1161,7 +1163,7 @@ async def test_cleanup3(key) -> None:
 
     assert conn._cleanup_handle is not None
     loop.call_at.assert_called_with(319, mock.ANY, mock.ANY)
-    conn.close()
+    await conn.close()
 
 
 async def test_cleanup_closed(loop, mocker) -> None:
@@ -1314,14 +1316,14 @@ async def test_close_twice(loop) -> None:
 
     conn = aiohttp.BaseConnector(loop=loop)
     conn._conns[1] = [(proto, object())]
-    conn.close()
+    await conn.close()
 
     assert not conn._conns
     assert proto.close.called
     assert conn.closed
 
     conn._conns = "Invalid"  # fill with garbage
-    conn.close()
+    await conn.close()
     assert conn.closed
 
 
@@ -1329,7 +1331,7 @@ async def test_close_cancels_cleanup_handle(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop)
     conn._release(1, mock.Mock(should_close=False))
     assert conn._cleanup_handle is not None
-    conn.close()
+    await conn.close()
     assert conn._cleanup_handle is None
 
 
@@ -1338,7 +1340,7 @@ async def test_close_abort_closed_transports(loop) -> None:
 
     conn = aiohttp.BaseConnector(loop=loop)
     conn._cleanup_closed_transports.append(tr)
-    conn.close()
+    await conn.close()
 
     assert not conn._cleanup_closed_transports
     assert tr.abort.called
@@ -1348,7 +1350,7 @@ async def test_close_abort_closed_transports(loop) -> None:
 async def test_close_cancels_cleanup_closed_handle(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop, enable_cleanup_closed=True)
     assert conn._cleanup_closed_handle is not None
-    conn.close()
+    await conn.close()
     assert conn._cleanup_closed_handle is None
 
 
@@ -1397,7 +1399,7 @@ async def f():
     await asyncio.sleep(0)
     assert acquired
     await task
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_queued_operation_tracing(loop, key) -> None:
@@ -1443,7 +1445,7 @@ async def f():
     await asyncio.sleep(0.01)
     connection1.release()
     await task
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_reuseconn_tracing(loop, key) -> None:
@@ -1473,7 +1475,7 @@ async def test_connect_reuseconn_tracing(loop, key) -> None:
     on_connection_reuseconn.assert_called_with(
         session, trace_config_ctx, aiohttp.TraceConnectionReuseconnParams()
     )
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_with_limit_and_limit_per_host(loop, key) -> None:
@@ -1507,7 +1509,7 @@ async def f():
     await asyncio.sleep(0)
     assert acquired
     await task
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_with_no_limit_and_limit_per_host(loop, key) -> None:
@@ -1539,7 +1541,7 @@ async def f():
     await asyncio.sleep(0)
     assert acquired
     await task
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_with_no_limits(loop, key) -> None:
@@ -1571,7 +1573,7 @@ async def f():
     assert acquired
     connection1.release()
     await task
-    conn.close()
+    await conn.close()
 
 
 async def test_connect_with_limit_cancelled(loop) -> None:
@@ -1599,6 +1601,8 @@ async def test_connect_with_limit_cancelled(loop) -> None:
         await asyncio.wait_for(conn.connect(req, None, ClientTimeout()), 0.01)
     connection.close()
 
+    await conn.close()
+
 
 async def test_connect_with_capacity_release_waiters(loop) -> None:
     def check_with_exc(err):
@@ -1672,7 +1676,7 @@ async def f(start=True):
         await asyncio.wait(tasks)
 
     await f()
-    conn.close()
+    await conn.close()
 
     assert max_connections == num_connections
 
@@ -1735,7 +1739,7 @@ async def test_close_with_acquired_connection(loop) -> None:
     connection = await conn.connect(req, None, ClientTimeout())
 
     assert 1 == len(conn._acquired)
-    conn.close()
+    await conn.close()
     assert 0 == len(conn._acquired)
     assert conn.closed
     proto.close.assert_called_with()
@@ -1754,26 +1758,26 @@ async def test_limit_property(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop, limit=15)
     assert 15 == conn.limit
 
-    conn.close()
+    await conn.close()
 
 
 async def test_limit_per_host_property(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop, limit_per_host=15)
     assert 15 == conn.limit_per_host
 
-    conn.close()
+    await conn.close()
 
 
 async def test_limit_property_default(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop)
     assert conn.limit == 100
-    conn.close()
+    await conn.close()
 
 
 async def test_limit_per_host_property_default(loop) -> None:
     conn = aiohttp.BaseConnector(loop=loop)
     assert conn.limit_per_host == 0
-    conn.close()
+    await conn.close()
 
 
 async def test_force_close_and_explicit_keep_alive(loop) -> None:
@@ -2055,7 +2059,7 @@ async def handler(request):
     r.close()
 
     await session.close()
-    conn.close()
+    await conn.close()
 
 
 async def test_tcp_connector_uses_provided_local_addr(aiohttp_server) -> None:
@@ -2079,7 +2083,7 @@ async def handler(request):
     assert first_conn.transport.get_extra_info("sockname") == ("127.0.0.1", port)
     r.close()
     await session.close()
-    conn.close()
+    await conn.close()
 
 
 @pytest.mark.skipif(not hasattr(socket, "AF_UNIX"), reason="requires UNIX sockets")
@@ -2264,3 +2268,5 @@ async def allow_connection_and_add_dummy_waiter():
         await_connection_and_check_waiters(),
         allow_connection_and_add_dummy_waiter(),
     )
+
+    await connector.close()
diff --git a/tests/test_proxy.py b/tests/test_proxy.py
index 1cdcc72067c..25bcb647fa2 100644
--- a/tests/test_proxy.py
+++ b/tests/test_proxy.py
@@ -73,6 +73,8 @@ async def make_conn():
             ssl=None,
         )
 
+        conn.close()
+
     @mock.patch("aiohttp.connector.ClientRequest")
     def test_proxy_headers(self, ClientRequestMock) -> None:
         req = ClientRequest(
@@ -113,6 +115,8 @@ async def make_conn():
             ssl=None,
         )
 
+        conn.close()
+
     def test_proxy_auth(self) -> None:
         with self.assertRaises(ValueError) as ctx:
             ClientRequest(
diff --git a/tests/test_proxy_functional.py b/tests/test_proxy_functional.py
index 2f4ee56f0a7..e20a6961ac6 100644
--- a/tests/test_proxy_functional.py
+++ b/tests/test_proxy_functional.py
@@ -164,6 +164,9 @@ async def test_secure_https_proxy_absolute_path(
     await sess.close()
     await conn.close()
 
+    # https://docs.aiohttp.org/en/v3.8.0/client_advanced.html#graceful-shutdown
+    await asyncio.sleep(0.1)
+
 
 @secure_proxy_xfail_under_py310_except_macos(raises=AssertionError)
 @pytest.mark.xfail(
diff --git a/tests/test_run_app.py b/tests/test_run_app.py
index e03a5fd6c90..44b27132605 100644
--- a/tests/test_run_app.py
+++ b/tests/test_run_app.py
@@ -646,27 +646,29 @@ def test_run_app_multiple_preexisting_sockets(patched_loop) -> None:
 def test_sigint() -> None:
     skip_if_on_windows()
 
-    proc = subprocess.Popen(
-        [sys.executable, "-u", "-c", _script_test_signal], stdout=subprocess.PIPE
-    )
-    for line in proc.stdout:
-        if line.startswith(b"======== Running on"):
-            break
-    proc.send_signal(signal.SIGINT)
-    assert proc.wait() == 0
+    with subprocess.Popen(
+        [sys.executable, "-u", "-c", _script_test_signal],
+        stdout=subprocess.PIPE,
+    ) as proc:
+        for line in proc.stdout:
+            if line.startswith(b"======== Running on"):
+                break
+        proc.send_signal(signal.SIGINT)
+        assert proc.wait() == 0
 
 
 def test_sigterm() -> None:
     skip_if_on_windows()
 
-    proc = subprocess.Popen(
-        [sys.executable, "-u", "-c", _script_test_signal], stdout=subprocess.PIPE
-    )
-    for line in proc.stdout:
-        if line.startswith(b"======== Running on"):
-            break
-    proc.terminate()
-    assert proc.wait() == 0
+    with subprocess.Popen(
+        [sys.executable, "-u", "-c", _script_test_signal],
+        stdout=subprocess.PIPE,
+    ) as proc:
+        for line in proc.stdout:
+            if line.startswith(b"======== Running on"):
+                break
+        proc.terminate()
+        assert proc.wait() == 0
 
 
 def test_startup_cleanup_signals_even_on_failure(patched_loop) -> None:
diff --git a/tests/test_streams.py b/tests/test_streams.py
index b2f909a8797..01e12d90c9b 100644
--- a/tests/test_streams.py
+++ b/tests/test_streams.py
@@ -89,6 +89,12 @@ def test_ctor_global_loop(self) -> None:
 
         assert stream._loop is loop
 
+        # Cleanup, leaks into `test_at_eof` otherwise:
+        loop.stop()
+        loop.run_forever()
+        loop.close()
+        gc.collect()
+
     async def test_at_eof(self) -> None:
         stream = self._make_one()
         assert not stream.at_eof()
diff --git a/tests/test_web_app.py b/tests/test_web_app.py
index 9879fe83740..160d8ac81e7 100644
--- a/tests/test_web_app.py
+++ b/tests/test_web_app.py
@@ -1,4 +1,5 @@
 import asyncio
+import gc
 from unittest import mock
 
 import pytest
@@ -48,6 +49,12 @@ def test_set_loop_default_loop() -> None:
         assert app.loop is loop
     asyncio.set_event_loop(None)
 
+    # Cleanup, leaks into `test_app_make_handler_debug_exc[True]` otherwise:
+    loop.stop()
+    loop.run_forever()
+    loop.close()
+    gc.collect()
+
 
 def test_set_loop_with_different_loops() -> None:
     loop = asyncio.new_event_loop()
@@ -59,6 +66,12 @@ def test_set_loop_with_different_loops() -> None:
     with pytest.raises(RuntimeError):
         app._set_loop(loop=object())
 
+    # Cleanup, leaks into `test_app_make_handler_debug_exc[True]` otherwise:
+    loop.stop()
+    loop.run_forever()
+    loop.close()
+    gc.collect()
+
 
 @pytest.mark.parametrize("debug", [True, False])
 async def test_app_make_handler_debug_exc(mocker, debug) -> None:
diff --git a/tests/test_web_functional.py b/tests/test_web_functional.py
index 55dea84c301..88d0dfd1c7f 100644
--- a/tests/test_web_functional.py
+++ b/tests/test_web_functional.py
@@ -325,7 +325,8 @@ async def handler(request):
 
     fname = here / "data.unknown_mime_type"
 
-    resp = await client.post("/", data=[fname.open("rb")])
+    with fname.open("rb") as fd:
+        resp = await client.post("/", data=[fd])
     assert 200 == resp.status
 
 
@@ -876,12 +877,15 @@ async def handler(request):
 
 
 async def test_response_with_file(aiohttp_client, fname) -> None:
+    outer_file_descriptor = None
 
     with fname.open("rb") as f:
         data = f.read()
 
     async def handler(request):
-        return web.Response(body=fname.open("rb"))
+        nonlocal outer_file_descriptor
+        outer_file_descriptor = fname.open("rb")
+        return web.Response(body=outer_file_descriptor)
 
     app = web.Application()
     app.router.add_get("/", handler)
@@ -902,15 +906,21 @@ async def handler(request):
     assert resp.headers.get("Content-Length") == str(len(resp_data))
     assert resp.headers.get("Content-Disposition") == expected_content_disposition
 
+    outer_file_descriptor.close()
+
 
 async def test_response_with_file_ctype(aiohttp_client, fname) -> None:
+    outer_file_descriptor = None
 
     with fname.open("rb") as f:
         data = f.read()
 
     async def handler(request):
+        nonlocal outer_file_descriptor
+        outer_file_descriptor = fname.open("rb")
+
         return web.Response(
-            body=fname.open("rb"), headers={"content-type": "text/binary"}
+            body=outer_file_descriptor, headers={"content-type": "text/binary"}
         )
 
     app = web.Application()
@@ -928,14 +938,19 @@ async def handler(request):
     assert resp.headers.get("Content-Length") == str(len(resp_data))
     assert resp.headers.get("Content-Disposition") == expected_content_disposition
 
+    outer_file_descriptor.close()
+
 
 async def test_response_with_payload_disp(aiohttp_client, fname) -> None:
+    outer_file_descriptor = None
 
     with fname.open("rb") as f:
         data = f.read()
 
     async def handler(request):
-        pl = aiohttp.get_payload(fname.open("rb"))
+        nonlocal outer_file_descriptor
+        outer_file_descriptor = fname.open("rb")
+        pl = aiohttp.get_payload(outer_file_descriptor)
         pl.set_content_disposition("inline", filename="test.txt")
         return web.Response(body=pl, headers={"content-type": "text/binary"})
 
@@ -954,6 +969,8 @@ async def handler(request):
         == "inline; filename=\"test.txt\"; filename*=utf-8''test.txt"
     )
 
+    outer_file_descriptor.close()
+
 
 async def test_response_with_payload_stringio(aiohttp_client, fname) -> None:
     async def handler(request):
@@ -1566,6 +1583,7 @@ async def handler(request):
     assert (
         "Maximum request body size 10 exceeded, " "actual body size 1024" in resp_text
     )
+    data["file"].close()
 
 
 async def test_post_max_client_size_for_file(aiohttp_client) -> None:
@@ -1619,11 +1637,12 @@ async def handler(request):
 
     f = tmpdir.join("foobar.txt")
     f.write_text("test", encoding="utf8")
-    data = {"file": open(str(f), "rb")}
-    resp = await client.post("/", data=data)
+    with open(str(f), "rb") as fd:
+        data = {"file": fd}
+        resp = await client.post("/", data=data)
 
-    assert 200 == resp.status
-    body = await resp.read()
+        assert 200 == resp.status
+        body = await resp.read()
     assert body == b"test"
 
     disp = multipart.parse_content_disposition(resp.headers["content-disposition"])
@@ -1701,12 +1720,15 @@ async def handler(request):
     app = web.Application()
     app.router.add_route("GET", "/", handler)
     server = await aiohttp_server(app)
-    resp = await aiohttp.ClientSession().get(server.make_url("/"))
+    session = aiohttp.ClientSession()
+    resp = await session.get(server.make_url("/"))
     async with resp:
         assert resp.status == 200
         assert resp.connection is None
     assert resp.connection is None
 
+    await session.close()
+
 
 async def test_response_context_manager_error(aiohttp_server) -> None:
     async def handler(request):
@@ -1727,6 +1749,8 @@ async def handler(request):
 
     assert len(session._connector._conns) == 1
 
+    await session.close()
+
 
 async def aiohttp_client_api_context_manager(aiohttp_server):
     async def handler(request):
diff --git a/tests/test_web_urldispatcher.py b/tests/test_web_urldispatcher.py
index 354be354496..f27002883f6 100644
--- a/tests/test_web_urldispatcher.py
+++ b/tests/test_web_urldispatcher.py
@@ -153,6 +153,7 @@ async def test_access_to_the_file_with_spaces(
     r = await client.get(url)
     assert r.status == 200
     assert (await r.text()) == data
+    await r.release()
 
 
 async def test_access_non_existing_resource(tmp_dir_path, aiohttp_client) -> None: