diff --git a/Doc/library/inspect.rst b/Doc/library/inspect.rst
--- a/Doc/library/inspect.rst
+++ b/Doc/library/inspect.rst
@@ -795,6 +795,16 @@
    .. versionadded:: 3.3
 
 
+.. function:: unwrap(func)
+
+   Get the object wrapped by *func*. It follows the chain of :attr:`__wrapped__`
+   attributes returning the last object in the chain.
+
+   :exc:`ValueError` is raised if a cycle is encountered.
+
+   .. versionadded:: 3.4
+
+
 .. _inspect-stack:
 
 The interpreter stack
diff --git a/Lib/inspect.py b/Lib/inspect.py
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -361,6 +361,25 @@
     "Return tuple of base classes (including cls) in method resolution order."
     return cls.__mro__
 
+# -------------------------------------------------------- function helpers
+
+def unwrap(func):
+    """Get the object wrapped by 'func'.
+
+    Follow the chain of __wrapped__ attributes,
+    and return the last object in the chain.
+    If there is a cycle, raise a ValueError.
+    """
+    f = func  # remember the original func for error reporting
+    memo = {id(func)}
+    while hasattr(func, '__wrapped__'):
+        func = func.__wrapped__
+        if id(func) in memo:
+            raise ValueError('wrapper loop when unwrapping {!r}'.format(f))
+        else:
+            memo.add(id(func))
+    return func
+
 # -------------------------------------------------- source code extraction
 def indentsize(line):
     """Return the indent size, in spaces, at the start of a line of text."""
@@ -1352,13 +1371,8 @@
         if sig is not None:
             return sig
 
-    try:
-        # Was this function wrapped by a decorator?
-        wrapped = obj.__wrapped__
-    except AttributeError:
-        pass
-    else:
-        return signature(wrapped)
+    # Was this function wrapped by a decorator?
+    obj = unwrap(obj)
 
     if isinstance(obj, types.FunctionType):
         return Signature.from_function(obj)
diff --git a/Lib/test/test_inspect.py b/Lib/test/test_inspect.py
--- a/Lib/test/test_inspect.py
+++ b/Lib/test/test_inspect.py
@@ -8,6 +8,7 @@
 import collections
 import os
 import shutil
+import functools
 from os.path import normcase
 
 from test.support import run_unittest, TESTFN, DirsOnSysPath
@@ -1827,6 +1828,10 @@
         self.assertEqual(self.signature(Wrapped),
                          ((('a', ..., ..., "positional_or_keyword"),),
                           ...))
+        # wrapper loop:
+        Wrapped.__wrapped__ = Wrapped
+        with self.assertRaisesRegex(ValueError, 'wrapper loop'):
+            self.signature(Wrapped)
 
     def test_signature_on_lambdas(self):
         self.assertEqual(self.signature((lambda a=10: a)),
@@ -2268,6 +2273,37 @@
         self.assertNotEqual(ba, ba4)
 
 
+class TestUnwrap(unittest.TestCase):
+
+    def test_unwrap(self):
+        def func(a, b):
+            return a + b
+        wrapper = functools.lru_cache(maxsize=20)(func)
+        self.assertIs(inspect.unwrap(wrapper), func)
+
+    def test_cycle(self):
+        def func1(): pass
+        func1.__wrapped__ = func1
+        with self.assertRaisesRegex(ValueError, 'wrapper loop'):
+            inspect.unwrap(func1)
+
+        def func2(): pass
+        func2.__wrapped__ = func1
+        func1.__wrapped__ = func2
+        with self.assertRaisesRegex(ValueError, 'wrapper loop'):
+            inspect.unwrap(func1)
+        with self.assertRaisesRegex(ValueError, 'wrapper loop'):
+            inspect.unwrap(func2)
+
+    def test_unhashable(self):
+        def func(): pass
+        func.__wrapped__ = None
+        class C:
+            __hash__ = None
+            __wrapped__ = func
+        self.assertIsNone(inspect.unwrap(C()))
+
+
 def test_main():
     run_unittest(
         TestDecorators, TestRetrievingSourceCode, TestOneliners, TestBuggyCases,
@@ -2275,7 +2311,7 @@
         TestGetcallargsFunctions, TestGetcallargsMethods,
         TestGetcallargsUnboundMethods, TestGetattrStatic, TestGetGeneratorState,
         TestNoEOL, TestSignatureObject, TestSignatureBind, TestParameterObject,
-        TestBoundArguments, TestGetClosureVars
+        TestBoundArguments, TestGetClosureVars, TestUnwrap
     )
 
 if __name__ == "__main__":