diff -r 18825546acbc Lib/ssl.py
--- a/Lib/ssl.py	Sun Sep 18 14:34:13 2016 +0200
+++ b/Lib/ssl.py	Sun Sep 18 20:49:00 2016 +0200
@@ -104,7 +104,7 @@
 from _ssl import _SSLContext, MemoryBIO, SSLSession
 from _ssl import (
     SSLError, SSLZeroReturnError, SSLWantReadError, SSLWantWriteError,
-    SSLSyscallError, SSLEOFError,
+    SSLSyscallError, SSLEOFError, SSLCertVerificationError
     )
 from _ssl import txt2obj as _txt2obj, nid2obj as _nid2obj
 from _ssl import RAND_status, RAND_add, RAND_bytes, RAND_pseudo_bytes
diff -r 18825546acbc Lib/test/test_ssl.py
--- a/Lib/test/test_ssl.py	Sun Sep 18 14:34:13 2016 +0200
+++ b/Lib/test/test_ssl.py	Sun Sep 18 20:49:00 2016 +0200
@@ -1489,8 +1489,10 @@
         s = test_wrap_socket(socket.socket(socket.AF_INET),
                             cert_reqs=ssl.CERT_REQUIRED)
         self.addCleanup(s.close)
-        self.assertRaisesRegex(ssl.SSLError, "certificate verify failed",
-                               s.connect, self.server_addr)
+        self.assertRaisesRegex(
+            ssl.SSLCertVerificationError,
+            "certificate verify failed: unable to get local issuer certificate",
+            s.connect, self.server_addr)
 
     def test_connect_ex(self):
         # Issue #11326: check connect_ex() implementation
@@ -1553,8 +1555,10 @@
         ctx.verify_mode = ssl.CERT_REQUIRED
         s = ctx.wrap_socket(socket.socket(socket.AF_INET))
         self.addCleanup(s.close)
-        self.assertRaisesRegex(ssl.SSLError, "certificate verify failed",
-                                s.connect, self.server_addr)
+        self.assertRaisesRegex(
+            ssl.SSLCertVerificationError,
+            "certificate verify failed: unable to get local issuer certificate",
+            s.connect, self.server_addr)
 
     def test_connect_capath(self):
         # Verify server certificates using the `capath` argument
@@ -2405,8 +2409,9 @@
             server = ThreadedEchoServer(context=server_context, chatty=True)
             with server:
                 with context.wrap_socket(socket.socket()) as s:
-                    with self.assertRaisesRegex(ssl.SSLError,
-                                                "certificate verify failed"):
+                    with self.assertRaisesRegex(
+                            ssl.SSLCertVerificationError,
+                            "certificate verify failed: unable to get certificate CRL"):
                         s.connect((HOST, server.port))
 
             # now load a CRL file. The CRL file is signed by the CA.
diff -r 18825546acbc Modules/_ssl.c
--- a/Modules/_ssl.c	Sun Sep 18 14:34:13 2016 +0200
+++ b/Modules/_ssl.c	Sun Sep 18 20:49:00 2016 +0200
@@ -76,6 +76,7 @@
 
 /* SSL error object */
 static PyObject *PySSLErrorObject;
+static PyObject *PySSLCertVerificationErrorObject;
 static PyObject *PySSLZeroReturnErrorObject;
 static PyObject *PySSLWantReadErrorObject;
 static PyObject *PySSLWantWriteErrorObject;
@@ -368,6 +369,9 @@
 PyDoc_STRVAR(SSLError_doc,
 "An error occurred in the SSL implementation.");
 
+PyDoc_STRVAR(SSLCertVerificationError_doc,
+"A certificate could not be verified.");
+
 PyDoc_STRVAR(SSLZeroReturnError_doc,
 "SSL/TLS session closed cleanly.");
 
@@ -413,9 +417,10 @@
 
 static void
 fill_and_set_sslerror(PyObject *type, int ssl_errno, const char *errstr,
-                      int lineno, unsigned long errcode)
+                      int lineno, unsigned long errcode, long verify_code)
 {
     PyObject *err_value = NULL, *reason_obj = NULL, *lib_obj = NULL;
+    const char *verify_str = NULL;
     PyObject *init_value, *msg, *key;
     _Py_IDENTIFIER(reason);
     _Py_IDENTIFIER(library);
@@ -447,15 +452,23 @@
     }
     if (errstr == NULL)
         errstr = "unknown error";
-
-    if (reason_obj && lib_obj)
+    if (verify_code != -1) {
+        verify_str = X509_verify_cert_error_string(verify_code);
+    }
+
+    if (verify_str && reason_obj && lib_obj) {
+        msg = PyUnicode_FromFormat("[%S: %S] %s: %s (_ssl.c:%d)",
+                                   lib_obj, reason_obj, errstr, verify_str,
+                                   lineno);
+    } else if (reason_obj && lib_obj) {
         msg = PyUnicode_FromFormat("[%S: %S] %s (_ssl.c:%d)",
                                    lib_obj, reason_obj, errstr, lineno);
-    else if (lib_obj)
+    } else if (lib_obj) {
         msg = PyUnicode_FromFormat("[%S] %s (_ssl.c:%d)",
                                    lib_obj, errstr, lineno);
-    else
+    } else {
         msg = PyUnicode_FromFormat("%s (_ssl.c:%d)", errstr, lineno);
+    }
     if (msg == NULL)
         goto fail;
 
@@ -487,6 +500,7 @@
     PyObject *type = PySSLErrorObject;
     char *errstr = NULL;
     int err;
+    long verify_code = -1;
     enum py_ssl_error p = PY_SSL_ERROR_NONE;
     unsigned long e = 0;
 
@@ -551,6 +565,11 @@
             if (e == 0)
                 /* possible? */
                 errstr = "A failure in the SSL library occurred";
+            if (ERR_GET_LIB(e) == ERR_LIB_SSL &&
+                    ERR_GET_REASON(e) == SSL_R_CERTIFICATE_VERIFY_FAILED) {
+                type = PySSLCertVerificationErrorObject;
+                verify_code = SSL_get_verify_result(obj->ssl);
+            }
             break;
         }
         default:
@@ -558,7 +577,7 @@
             errstr = "Invalid error code";
         }
     }
-    fill_and_set_sslerror(type, p, errstr, lineno, e);
+    fill_and_set_sslerror(type, p, errstr, lineno, e, verify_code);
     ERR_clear_error();
     return NULL;
 }
@@ -570,7 +589,7 @@
         errcode = ERR_peek_last_error();
     else
         errcode = 0;
-    fill_and_set_sslerror(PySSLErrorObject, errcode, errstr, lineno, errcode);
+    fill_and_set_sslerror(PySSLErrorObject, errcode, errstr, lineno, errcode, -1);
     ERR_clear_error();
     return NULL;
 }
@@ -5190,6 +5209,9 @@
     if (PySSLErrorObject == NULL)
         return NULL;
 
+    PySSLCertVerificationErrorObject = PyErr_NewExceptionWithDoc(
+        "ssl.SSLCertVerificationError", SSLCertVerificationError_doc,
+        PySSLErrorObject, NULL);
     PySSLZeroReturnErrorObject = PyErr_NewExceptionWithDoc(
         "ssl.SSLZeroReturnError", SSLZeroReturnError_doc,
         PySSLErrorObject, NULL);
@@ -5205,13 +5227,16 @@
     PySSLEOFErrorObject = PyErr_NewExceptionWithDoc(
         "ssl.SSLEOFError", SSLEOFError_doc,
         PySSLErrorObject, NULL);
-    if (PySSLZeroReturnErrorObject == NULL
+    if (PySSLCertVerificationErrorObject == NULL
+        || PySSLZeroReturnErrorObject == NULL
         || PySSLWantReadErrorObject == NULL
         || PySSLWantWriteErrorObject == NULL
         || PySSLSyscallErrorObject == NULL
         || PySSLEOFErrorObject == NULL)
         return NULL;
     if (PyDict_SetItemString(d, "SSLError", PySSLErrorObject) != 0
+        || PyDict_SetItemString(d, "SSLCertVerificationError",
+                                PySSLCertVerificationErrorObject) != 0
         || PyDict_SetItemString(d, "SSLZeroReturnError", PySSLZeroReturnErrorObject) != 0
         || PyDict_SetItemString(d, "SSLWantReadError", PySSLWantReadErrorObject) != 0
         || PyDict_SetItemString(d, "SSLWantWriteError", PySSLWantWriteErrorObject) != 0