diff --git a/Lib/socket.py b/Lib/socket.py
index 96f8ed0..475a18c 100644
--- a/Lib/socket.py
+++ b/Lib/socket.py
@@ -48,6 +48,7 @@ import _socket
 from _socket import *
 
 import os, sys, io
+from enum import IntEnum
 
 try:
     import errno
@@ -60,6 +61,28 @@ EWOULDBLOCK = getattr(errno, 'EWOULDBLOCK', 11)
 __all__ = ["getfqdn", "create_connection"]
 __all__.extend(os._get_exports_list(_socket))
 
+# Set up the socket.AF_* constants as members of an IntEnum for nicer string
+# representations.
+# Since not all AF_* constants are actually defined by the underlying _socket
+# extension on all platforms, this has to be done carefully, by examining the
+# constants that did get imported into this module's globals by
+# 'from socket import *'. Those constants get replaced by corresponding enum
+# members.
+# Note that _socket only knows about the integer values. The public interface
+# in this module understands the enums and translates them back from integers
+# where needed (e.g. .family property of a socket object).
+_potential_af_names = ['AF_INET', 'AF_INET6', 'AF_UNIX', 'AF_RDS', 'AF_CAN',
+                       'AF_LINK', 'AF_UNSPEC', 'AF_AX25', 'AF_IPX', 'AF_NETROM',
+                       'AF_BRIDGE', 'AD_ATMPVC', 'AF_AAL5', 'AF_X25', 'AF_ROSE',
+                       'AF_DECnet', 'AF_NETBEUI', 'AF_SECURITY', 'AF_PACKET',
+                       'AF_NETLINK', 'AF_ROUTE', 'AF_ASH', 'AF_ECONET',
+                       'AF_ATMSVC', 'AF_SNA', 'AF_IRDA', 'AF_PPPOX', 'AF_KEY',
+                       'AF_WANPIPE', 'AF_LLC', 'AF_BLUETOOTH', 'AF_SYSTEM']
+_moduledict = globals()
+_af_dict = {name: _moduledict[name] for name in _potential_af_names
+                                    if name in _moduledict}
+AddressFamily = IntEnum('AddressFamily', _af_dict)
+_moduledict.update(AddressFamily.__members__)
 
 _realsocket = socket
 
@@ -91,6 +114,10 @@ class socket(_socket.socket):
     __slots__ = ["__weakref__", "_io_refs", "_closed"]
 
     def __init__(self, family=AF_INET, type=SOCK_STREAM, proto=0, fileno=None):
+        # For user code address family values are members of AddressFamily, but
+        # for the underlying _socket.socket they're just integers. The
+        # constructor of _socket.socket converts the given family argument to an
+        # integer automatically.
         _socket.socket.__init__(self, family, type, proto, fileno)
         self._io_refs = 0
         self._closed = False
@@ -229,6 +256,13 @@ class socket(_socket.socket):
         self._closed = True
         return super().detach()
 
+    @property
+    def family(self):
+        """Read-only access to the address family for this socket.
+        """
+        return AddressFamily(super().family)
+
+
 def fromfd(fd, family, type, proto=0):
     """ fromfd(fd, family, type[, proto]) -> socket object
 
diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 54fb9a1..80e941b 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -664,6 +664,11 @@ class GeneralModuleTests(unittest.TestCase):
         self.assertIn('[closed]', repr(s))
         self.assertNotIn('laddr', repr(s))
 
+    def test_str_for_enums(self):
+        # Make sure that the AF_* constants have enum-like string reprs.
+        with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as s:
+            self.assertEqual(str(s.family), 'AddressFamily.AF_INET')
+
     def test_weakref(self):
         s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
         p = proxy(s)