diff --git a/stdlib/socketserver.pyi b/stdlib/socketserver.pyi
index f0617e393..8c759aaf9 100644
--- a/stdlib/socketserver.pyi
+++ b/stdlib/socketserver.pyi
@@ -1,7 +1,7 @@
 import sys
 import types
 from socket import SocketType
-from typing import Any, BinaryIO, Callable, ClassVar, List, Optional, Tuple, Type, TypeVar, Union
+from typing import Any, BinaryIO, Callable, ClassVar, Optional, Set, Tuple, Type, TypeVar, Union
 
 _T = TypeVar("_T")
 
@@ -20,19 +20,29 @@ class BaseServer:
     def serve_forever(self, poll_interval: float = ...) -> None: ...
     def shutdown(self) -> None: ...
     def server_close(self) -> None: ...
-    def finish_request(self, request: bytes, client_address: Tuple[str, int]) -> None: ...
-    def get_request(self) -> Tuple[SocketType, Tuple[str, int]]: ...
-    def handle_error(self, request: bytes, client_address: Tuple[str, int]) -> None: ...
+    def finish_request(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> None: ...
+    def get_request(self) -> Tuple[Any, Any]: ...
+    def handle_error(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> None: ...
     def handle_timeout(self) -> None: ...
-    def process_request(self, request: bytes, client_address: Tuple[str, int]) -> None: ...
+    def process_request(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> None: ...
     def server_activate(self) -> None: ...
     def server_bind(self) -> None: ...
-    def verify_request(self, request: bytes, client_address: Tuple[str, int]) -> bool: ...
+    def verify_request(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> bool: ...
     def __enter__(self: _T) -> _T: ...
     def __exit__(
         self, exc_type: Optional[Type[BaseException]], exc_val: Optional[BaseException], exc_tb: Optional[types.TracebackType]
     ) -> None: ...
     def service_actions(self) -> None: ...
+    def shutdown_request(self, request: Union[SocketType, Tuple[bytes, SocketType]]) -> None: ...  # undocumented
+    def close_request(self, request: Union[SocketType, Tuple[bytes, SocketType]]) -> None: ...  # undocumented
 
 class TCPServer(BaseServer):
     def __init__(
@@ -41,6 +51,13 @@ class TCPServer(BaseServer):
         RequestHandlerClass: Callable[..., BaseRequestHandler],
         bind_and_activate: bool = ...,
     ) -> None: ...
+    def get_request(self) -> Tuple[SocketType, Any]: ...
+    def finish_request(self, request: SocketType, client_address: Union[Tuple[str, int], str]) -> None: ...
+    def handle_error(self, request: SocketType, client_address: Union[Tuple[str, int], str]) -> None: ...
+    def process_request(self, request: SocketType, client_address: Union[Tuple[str, int], str]) -> None: ...
+    def verify_request(self, request: SocketType, client_address: Union[Tuple[str, int], str]) -> bool: ...
+    def shutdown_request(self, request: SocketType) -> None: ...  # undocumented
+    def close_request(self, request: SocketType) -> None: ...  # undocumented
 
 class UDPServer(BaseServer):
     def __init__(
@@ -49,6 +66,13 @@ class UDPServer(BaseServer):
         RequestHandlerClass: Callable[..., BaseRequestHandler],
         bind_and_activate: bool = ...,
     ) -> None: ...
+    def get_request(self) -> Tuple[Tuple[bytes, SocketType], Any]: ...
+    def finish_request(self, request: Tuple[bytes, SocketType], client_address: Union[Tuple[str, int], str]) -> None: ...
+    def handle_error(self, request: Tuple[bytes, SocketType], client_address: Union[Tuple[str, int], str]) -> None: ...
+    def process_request(self, request: Tuple[bytes, SocketType], client_address: Union[Tuple[str, int], str]) -> None: ...
+    def verify_request(self, request: Tuple[bytes, SocketType], client_address: Union[Tuple[str, int], str]) -> bool: ...
+    def shutdown_request(self, request: Tuple[bytes, SocketType]) -> None: ...  # undocumented
+    def close_request(self, request: Tuple[bytes, SocketType]) -> None: ...  # undocumented
 
 if sys.platform != "win32":
     class UnixStreamServer(BaseServer):
@@ -69,22 +93,28 @@ if sys.platform != "win32":
 if sys.platform != "win32":
     class ForkingMixIn:
         timeout: Optional[float]  # undocumented
-        active_children: Optional[List[int]]  # undocumented
+        active_children: Optional[Set[int]]  # undocumented
         max_children: int  # undocumented
         if sys.version_info >= (3, 7):
             block_on_close: bool
         def collect_children(self, *, blocking: bool = ...) -> None: ...  # undocumented
         def handle_timeout(self) -> None: ...  # undocumented
         def service_actions(self) -> None: ...  # undocumented
-        def process_request(self, request: bytes, client_address: Tuple[str, int]) -> None: ...
+        def process_request(
+            self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+        ) -> None: ...
         def server_close(self) -> None: ...
 
 class ThreadingMixIn:
     daemon_threads: bool
     if sys.version_info >= (3, 7):
         block_on_close: bool
-    def process_request_thread(self, request: bytes, client_address: Tuple[str, int]) -> None: ...  # undocumented
-    def process_request(self, request: bytes, client_address: Tuple[str, int]) -> None: ...
+    def process_request_thread(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> None: ...  # undocumented
+    def process_request(
+        self, request: Union[SocketType, Tuple[bytes, SocketType]], client_address: Union[Tuple[str, int], str]
+    ) -> None: ...
     def server_close(self) -> None: ...
 
 if sys.platform != "win32":
@@ -108,7 +138,12 @@ class BaseRequestHandler:
     request: Any
     client_address: Any
     server: BaseServer
-    def __init__(self, request: Any, client_address: Any, server: BaseServer) -> None: ...
+    def __init__(
+        self,
+        request: Union[SocketType, Tuple[bytes, SocketType]],
+        client_address: Union[Tuple[str, int], str],
+        server: BaseServer,
+    ) -> None: ...
     def setup(self) -> None: ...
     def handle(self) -> None: ...
     def finish(self) -> None: ...