--- a/Modules/_hashopenssl.c
+++ b/Modules/_hashopenssl.c
@@ -1071,7 +1071,7 @@ PyInit__hashlib(void)
 {
     PyObject *m, *openssl_md_meth_names;
 
-#ifndef OPENSSL_VERSION_1_1
+#if OPENSSL_VERSION_NUMBER < 0x10100000L
     /* Load all digest algorithms and initialize cpuid */
     OPENSSL_add_all_algorithms_noconf();
     ERR_load_crypto_strings();
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -47,6 +47,7 @@ static PySocketModule_APIObject PySocketModule;
 
 /* Include OpenSSL header files */
 #include "openssl/rsa.h"
+#include "openssl/dh.h"
 #include "openssl/crypto.h"
 #include "openssl/x509.h"
 #include "openssl/x509v3.h"
@@ -128,13 +129,13 @@ static void _PySSLFixErrno(void) {
 #include "_ssl_data.h"
 
 #if (OPENSSL_VERSION_NUMBER >= 0x10100000L) && !defined(LIBRESSL_VERSION_NUMBER)
-#  define OPENSSL_VERSION_1_1 1
-#  define PY_OPENSSL_1_1_API 1
+# define OPENSSL_VERSION_1_1 1
+# define PY_OPENSSL_1_1_API 1
 #endif
 
 /* LibreSSL 2.7.0 provides necessary OpenSSL 1.1.0 APIs */
 #if defined(LIBRESSL_VERSION_NUMBER) && LIBRESSL_VERSION_NUMBER >= 0x2070000fL
-#  define PY_OPENSSL_1_1_API 1
+# define PY_OPENSSL_1_1_API 1
 #endif
 
 /* Openssl comes with TLSv1.1 and TLSv1.2 between 1.0.0h and 1.0.1
@@ -197,6 +198,11 @@ static void _PySSLFixErrno(void) {
 #define TLS_method SSLv23_method
 #define TLS_client_method SSLv23_client_method
 #define TLS_server_method SSLv23_server_method
+#define X509_getm_notBefore X509_get_notBefore
+#define X509_getm_notAfter X509_get_notAfter
+#define OpenSSL_version_num SSLeay
+#define OpenSSL_version SSLeay_version
+#define OPENSSL_VERSION SSLEAY_VERSION
 
 static int X509_NAME_ENTRY_set(const X509_NAME_ENTRY *ne)
 {
@@ -859,7 +865,7 @@ _ssl_configure_hostname(PySSLSocket *self, const char* server_hostname)
                 goto error;
             }
         } else {
-            if (!X509_VERIFY_PARAM_set1_ip(param, ASN1_STRING_data(ip),
+            if (!X509_VERIFY_PARAM_set1_ip(param, ASN1_STRING_get0_data(ip),
                                            ASN1_STRING_length(ip))) {
                 _setSSLError(NULL, 0, __FILE__, __LINE__);
                 goto error;
@@ -1624,7 +1630,7 @@ _decode_certificate(X509 *certificate) {
     Py_DECREF(sn_obj);
 
     (void) BIO_reset(biobuf);
-    notBefore = X509_get_notBefore(certificate);
+    notBefore = X509_getm_notBefore(certificate);
     ASN1_TIME_print(biobuf, notBefore);
     len = BIO_gets(biobuf, buf, sizeof(buf)-1);
     if (len < 0) {
@@ -1641,7 +1647,7 @@ _decode_certificate(X509 *certificate) {
     Py_DECREF(pnotBefore);
 
     (void) BIO_reset(biobuf);
-    notAfter = X509_get_notAfter(certificate);
+    notAfter = X509_getm_notAfter(certificate);
     ASN1_TIME_print(biobuf, notAfter);
     len = BIO_gets(biobuf, buf, sizeof(buf)-1);
     if (len < 0) {
@@ -3152,7 +3158,7 @@ _ssl__SSLContext_impl(PyTypeObject *type, int proto_version)
        conservative and assume it wasn't fixed until release. We do this check
        at runtime to avoid problems from the dynamic linker.
        See #25672 for more on this. */
-    libver = SSLeay();
+    libver = OpenSSL_version_num();
     if (!(libver >= 0x10001000UL && libver < 0x1000108fUL) &&
         !(libver >= 0x10000000UL && libver < 0x100000dfUL)) {
         SSL_CTX_set_mode(self->ctx, SSL_MODE_RELEASE_BUFFERS);
@@ -5159,7 +5175,7 @@ PySSL_RAND(int len, int pseudo)
     if (bytes == NULL)
         return NULL;
     if (pseudo) {
-        ok = RAND_pseudo_bytes((unsigned char*)PyBytes_AS_STRING(bytes), len);
+        ok = RAND_bytes((unsigned char*)PyBytes_AS_STRING(bytes), len);
         if (ok == 0 || ok == 1)
             return Py_BuildValue("NO", bytes, ok == 1 ? Py_True : Py_False);
     }
@@ -6176,10 +6192,10 @@ PyInit__ssl(void)
         return NULL;
 
     /* OpenSSL version */
-    /* SSLeay() gives us the version of the library linked against,
+    /* OpenSSL_version_num() gives us the version of the library linked against,
        which could be different from the headers version.
     */
-    libver = SSLeay();
+    libver = OpenSSL_version_num();
     r = PyLong_FromUnsignedLong(libver);
     if (r == NULL)
         return NULL;
@@ -6199,7 +6205,7 @@ PyInit__ssl(void)
     r = Py_BuildValue("IIIII", major, minor, fix, patch, status);
     if (r == NULL || PyModule_AddObject(m, "OPENSSL_VERSION_INFO", r))
         return NULL;
-    r = PyUnicode_FromString(SSLeay_version(SSLEAY_VERSION));
+    r = PyUnicode_FromString(OpenSSL_version(OPENSSL_VERSION));
     if (r == NULL || PyModule_AddObject(m, "OPENSSL_VERSION", r))
         return NULL;