diff --git a/Lib/gzip.py b/Lib/gzip.py
index 08f9da5..f9a59d7 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -147,7 +147,7 @@
 
     def _init_write(self, filename):
         self.name = filename
-        self.crc = zlib.crc32("") & 0xffffffff
+        self.crc = zlib.crc32(b"") & 0xffffffff
         self.size = 0
         self.writebuf = []
         self.bufsize = 0
@@ -178,7 +178,7 @@
             self.fileobj.write(fname + b'\000')
 
     def _init_read(self):
-        self.crc = zlib.crc32("") & 0xffffffff
+        self.crc = zlib.crc32(b"") & 0xffffffff
         self.size = 0
 
     def _read_gzip_header(self):
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 7a67e15..7f08a98 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -410,7 +410,7 @@
             except ImportError:
                 raise CompressionError("zlib module is not available")
             self.zlib = zlib
-            self.crc = zlib.crc32("")
+            self.crc = zlib.crc32(b"")
             if mode == "r":
                 self._init_read_gz()
             else:
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 3718ca7..776557e 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -41,12 +41,12 @@
         self.assertEqual(zlib.adler32(b"penguin"),zlib.adler32(b"penguin",1))
 
     def test_crc32_adler32_unsigned(self):
-        foo = 'abcdefghijklmnop'
+        foo = b'abcdefghijklmnop'
         # explicitly test signed behavior
         self.assertEqual(zlib.crc32(foo), 2486878355)
-        self.assertEqual(zlib.crc32('spam'), 1138425661)
+        self.assertEqual(zlib.crc32(b'spam'), 1138425661)
         self.assertEqual(zlib.adler32(foo+foo), 3573550353)
-        self.assertEqual(zlib.adler32('spam'), 72286642)
+        self.assertEqual(zlib.adler32(b'spam'), 72286642)
 
     def test_same_as_binascii_crc32(self):
         foo = b'abcdefghijklmnop'
@@ -63,7 +63,18 @@
         # specifying compression level out of range causes an error
         # (but -1 is Z_DEFAULT_COMPRESSION and apparently the zlib
         # accepts 0 too)
-        self.assertRaises(zlib.error, zlib.compress, 'ERROR', 10)
+        self.assertRaises(zlib.error, zlib.compress, b'ERROR', 10)
+
+    def test_badargs(self):
+        self.assertRaises(TypeError, zlib.adler32)
+        self.assertRaises(TypeError, zlib.crc32)
+        self.assertRaises(TypeError, zlib.compress)
+        self.assertRaises(TypeError, zlib.decompress)
+        for arg in (42, None, '', 'abc', (), []):
+            self.assertRaises(TypeError, zlib.adler32, arg)
+            self.assertRaises(TypeError, zlib.crc32, arg)
+            self.assertRaises(TypeError, zlib.compress, arg)
+            self.assertRaises(TypeError, zlib.decompress, arg)
 
     def test_badcompressobj(self):
         # verify failure on building compress object with bad params
@@ -93,8 +104,9 @@
         # compress more data
         data = HAMLET_SCENE * 128
         x = zlib.compress(data)
-        self.assertEqual(zlib.decompress(x), data)
-
+        self.assertEqual(zlib.compress(bytearray(data)), x)
+        for ob in x, bytearray(x):
+            self.assertEqual(zlib.decompress(ob), data)
 
 
 
@@ -102,17 +114,22 @@
     # Test compression object
     def test_pair(self):
         # straightforward compress/decompress objects
-        data = HAMLET_SCENE * 128
-        co = zlib.compressobj()
-        x1 = co.compress(data)
-        x2 = co.flush()
-        self.assertRaises(zlib.error, co.flush) # second flush should not work
-        dco = zlib.decompressobj()
-        y1 = dco.decompress(x1 + x2)
-        y2 = dco.flush()
-        self.assertEqual(data, y1 + y2)
-        self.assertTrue(isinstance(dco.unconsumed_tail, bytes))
-        self.assertTrue(isinstance(dco.unused_data, bytes))
+        datasrc = HAMLET_SCENE * 128
+        datazip = zlib.compress(datasrc)
+        # should compress both bytes and bytearray data
+        for data in (datasrc, bytearray(datasrc)):
+            co = zlib.compressobj()
+            x1 = co.compress(data)
+            x2 = co.flush()
+            self.assertRaises(zlib.error, co.flush) # second flush should not work
+            self.assertEqual(x1 + x2, datazip)
+        for v1, v2 in ((x1, x2), (bytearray(x1), bytearray(x2))):
+            dco = zlib.decompressobj()
+            y1 = dco.decompress(v1 + v2)
+            y2 = dco.flush()
+            self.assertEqual(data, y1 + y2)
+            self.assertIsInstance(dco.unconsumed_tail, bytes)
+            self.assertIsInstance(dco.unused_data, bytes)
 
     def test_compressoptions(self):
         # specify lots of options to compressobj()
@@ -173,7 +190,7 @@
             bufs.append(dco.flush())
         else:
             while True:
-                chunk = dco.decompress('')
+                chunk = dco.decompress(b'')
                 if chunk:
                     bufs.append(chunk)
                 else:
@@ -241,7 +258,7 @@
             bufs.append(dco.flush())
         else:
             while chunk:
-                chunk = dco.decompress('', max_length)
+                chunk = dco.decompress(b'', max_length)
                 self.assertFalse(len(chunk) > max_length,
                             'chunk too big (%d>%d)' % (len(chunk),max_length))
                 bufs.append(chunk)
@@ -253,7 +270,7 @@
     def test_maxlenmisc(self):
         # Misc tests of max_length
         dco = zlib.decompressobj()
-        self.assertRaises(ValueError, dco.decompress, "", -1)
+        self.assertRaises(ValueError, dco.decompress, b"", -1)
         self.assertEqual(b'', dco.unconsumed_tail)
 
     def test_flushes(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index 335460a..e4c13a3 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -157,6 +157,10 @@
 Library
 -------
 
+- Issue #4757: `zlib.compress` and other methods in the zlib module now
+  raise a TypeError when given an `str` object (rather than a `bytes`-like
+  object).  Patch by Victor Stinner and Florent Xicluna.
+
 - Issue #7349: Make methods of file objects in the io module accept None as an
   argument where file-like objects (ie StringIO and BytesIO) accept them to mean
   the same as passing no argument.
diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index 6b818e5..2f2e214 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -107,7 +107,7 @@
     z_stream zst;
 
     /* require Python string object, optional 'level' arg */
-    if (!PyArg_ParseTuple(args, "s*|i:compress", &pinput, &level))
+    if (!PyArg_ParseTuple(args, "y*|i:compress", &pinput, &level))
 	return NULL;
     input = pinput.buf;
     length = pinput.len;
@@ -190,7 +190,7 @@
     Py_ssize_t r_strlen=DEFAULTALLOC;
     z_stream zst;
 
-    if (!PyArg_ParseTuple(args, "s*|in:decompress",
+    if (!PyArg_ParseTuple(args, "y*|in:decompress",
 			  &pinput, &wsize, &r_strlen))
 	return NULL;
     input = pinput.buf;
@@ -402,7 +402,7 @@
     Byte *input;
     unsigned long start_total_out;
 
-    if (!PyArg_ParseTuple(args, "s*:compress", &pinput))
+    if (!PyArg_ParseTuple(args, "y*:compress", &pinput))
 	return NULL;
     input = pinput.buf;
     inplen = pinput.len;
@@ -484,7 +484,7 @@
     Byte *input;
     unsigned long start_total_out;
 
-    if (!PyArg_ParseTuple(args, "s*|i:decompress", &pinput,
+    if (!PyArg_ParseTuple(args, "y*|i:decompress", &pinput,
 			  &max_length))
 	return NULL;
     input = pinput.buf;
@@ -912,8 +912,8 @@
     unsigned int adler32val = 1;  /* adler32(0L, Z_NULL, 0) */
     Py_buffer pbuf;
 
-    if (!PyArg_ParseTuple(args, "s*|I:adler32", &pbuf, &adler32val))
-	return NULL;
+    if (!PyArg_ParseTuple(args, "y*|I:adler32", &pbuf, &adler32val))
+        return NULL;
     /* Releasing the GIL for very small buffers is inefficient
        and may lower performance */
     if (pbuf.len > 1024*5) {
@@ -921,7 +921,7 @@
         adler32val = adler32(adler32val, pbuf.buf, pbuf.len);
         Py_END_ALLOW_THREADS
     } else {
-        adler32val = adler32(adler32val, pbuf.buf, pbuf.len);    
+        adler32val = adler32(adler32val, pbuf.buf, pbuf.len);
     }
     PyBuffer_Release(&pbuf);
     return PyLong_FromUnsignedLong(adler32val & 0xffffffffU);
@@ -940,7 +940,7 @@
     Py_buffer pbuf;
     int signed_val;
 
-    if (!PyArg_ParseTuple(args, "s*|I:crc32", &pbuf, &crc32val))
+    if (!PyArg_ParseTuple(args, "y*|I:crc32", &pbuf, &crc32val))
 	return NULL;
     /* Releasing the GIL for very small buffers is inefficient
        and may lower performance */