diff --git a/Doc/library/inspect.rst b/Doc/library/inspect.rst
index 4290aeb..694d3f2 100644
--- a/Doc/library/inspect.rst
+++ b/Doc/library/inspect.rst
@@ -429,11 +429,14 @@ function.
    Accepts a wide range of python callables, from plain functions and classes to
    :func:`functools.partial` objects.
 
+   Raises :exc:`ValueError` if no signature can be provided, and
+   :exc:`TypeError` if type of callable is not supported.
+
    .. note::
 
       Some callables may not be introspectable in certain implementations of
-      Python.  For example, in CPython, built-in functions defined in C provide
-      no metadata about their arguments.
+      Python.  For example, in CPython, some built-in functions defined in C
+      provide no metadata about their arguments.
 
 
 .. class:: Signature
diff --git a/Lib/inspect.py b/Lib/inspect.py
index d6bd8cd..c373276 100644
--- a/Lib/inspect.py
+++ b/Lib/inspect.py
@@ -1950,6 +1950,28 @@ class Signature:
 
     @classmethod
     def from_builtin(cls, func):
+        '''Constructs Signature for builtin functions'''
+
+        error_msg = 'no signature for builtin {!r}'.format(func)
+
+        try:
+            sig = cls._from_builtin(func)
+        except ValueError:
+            raise
+        except Exception:
+            # May be RuntimeError, TypeError, or something else.
+            # To make it more predictable, we wrap it in a single
+            # ValueError. And there is almost no point of having
+            # error context here, hence 'from None'.
+            raise ValueError(error_msg) from None
+
+        if sig is None:
+            raise ValueError(error_msg)
+
+        return sig
+
+    @classmethod
+    def _from_builtin(cls, func):
         s = getattr(func, "__text_signature__", None)
         if not s:
             return None
diff --git a/Lib/test/test_inspect.py b/Lib/test/test_inspect.py
index 1bfe724..093b13c 100644
--- a/Lib/test/test_inspect.py
+++ b/Lib/test/test_inspect.py
@@ -1594,9 +1594,6 @@ class TestSignatureObject(unittest.TestCase):
     @unittest.skipIf(MISSING_C_DOCSTRINGS,
                      "Signature information for builtins requires docstrings")
     def test_signature_on_builtins(self):
-        # min doesn't have a signature (yet)
-        self.assertEqual(inspect.signature(min), None)
-
         signature = inspect.signature(_testcapi.docstring_with_signature_with_defaults)
         self.assertTrue(isinstance(signature, inspect.Signature))
         def p(name): return signature.parameters[name].default
@@ -1611,6 +1608,10 @@ class TestSignatureObject(unittest.TestCase):
         self.assertEqual(p('sys'), sys.maxsize)
         self.assertEqual(p('exp'), sys.maxsize - 1)
 
+    def test_signature_on_builtins_no_signature(self):
+        with self.assertRaisesRegex(ValueError, 'no signature for builtin'):
+            inspect.signature(_testcapi.docstring_no_signature)
+
     def test_signature_on_non_function(self):
         with self.assertRaisesRegex(TypeError, 'is not a callable object'):
             inspect.signature(42)