@@ -1075,6 +1075,10 @@ def __getattr__(self, name):
             raise AttributeError
         return getattr(self._unbound.func, name)
 
+    @property
+    def __wrapped__(self):
+        return self._unbound.func
+
     @property
     def register(self):
         return self._unbound.register

diff --git a/Lib/inspect.py b/Lib/inspect.py
@@ -447,7 +447,8 @@ def isroutine(object):
             or isfunction(object)
             or ismethod(object)
             or ismethoddescriptor(object)
-            or ismethodwrapper(object))
+            or ismethodwrapper(object)
+            or isinstance(object, functools._singledispatchmethod_get))
 
 def isabstract(object):
     """Return true if the object is an abstract base class (ABC)."""

@@ -3312,6 +3312,58 @@ def t(self, arg):
             support.gc_collect()
         self.assertIsNone(r())
 
+    def test_signatures(self):
+        @functools.singledispatch
+        def func(item, arg: int) -> str:
+            return str(item)
+        @func.register
+        def _(item: int, arg: bytes) -> str:
+            return str(item)
+
+        self.assertEqual(str(Signature.from_callable(func)),
+                         '(item, arg: int) -> str')
+
+    def test_method_signatures(self):
+        class A:
+            def m(self, item, arg: int) -> str:
+                return str(item)
+            @classmethod
+            def cm(cls, item, arg: int) -> str:
+                return str(item)
+            @functools.singledispatchmethod
+            def func(self, item, arg: int) -> str:
+                return str(item)
+            @func.register
+            def _(self, item, arg: bytes) -> str:
+                return str(item)
+
+            @functools.singledispatchmethod
+            @classmethod
+            def cls_func(cls, item, arg: int) -> str:
+                return str(arg)
+            @func.register
+            @classmethod
+            def _(cls, item, arg: bytes) -> str:
+                return str(item)
+
+            @functools.singledispatchmethod
+            @staticmethod
+            def static_func(item, arg: int) -> str:
+                return str(arg)
+            @func.register
+            @staticmethod
+            def _(item, arg: bytes) -> str:
+                return str(item)
+
+        self.assertEqual(str(Signature.from_callable(A.func)),
+                         '(self, item, arg: int) -> str')
+        self.assertEqual(str(Signature.from_callable(A().func)),
+                         '(self, item, arg: int) -> str')
+        self.assertEqual(str(Signature.from_callable(A.cls_func)),
+                         '(cls, item, arg: int) -> str')
+        self.assertEqual(str(Signature.from_callable(A.static_func)),
+                         '(item, arg: int) -> str')
+
 
 class CachedCostItem:
     _cost = 1

diff --git a/Lib/test/test_inspect/test_inspect.py b/Lib/test/test_inspect/test_inspect.py
@@ -415,6 +415,27 @@ def test_isroutine(self):
         # partial
         self.assertTrue(inspect.isroutine(functools.partial(mod.spam)))
 
+    def test_isroutine_singledispatch(self):
+        self.assertTrue(inspect.isroutine(functools.singledispatch(mod.spam)))
+
+        class A:
+            @functools.singledispatchmethod
+            def method(self, arg):
+                pass
+            @functools.singledispatchmethod
+            @classmethod
+            def class_method(cls, arg):
+                pass
+            @functools.singledispatchmethod
+            @staticmethod
+            def static_method(arg):
+                pass
+
+        self.assertTrue(inspect.isroutine(A.method))
+        self.assertTrue(inspect.isroutine(A().method))
+        self.assertTrue(inspect.isroutine(A.static_method))
+        self.assertTrue(inspect.isroutine(A.class_method))
+
     def test_isclass(self):
         self.istest(inspect.isclass, 'mod.StupidGit')
         self.assertTrue(inspect.isclass(list))