A Semitic people, the Assyrians lived in the northern area of Mesopotamia, the land between the Tigris and Euphrates Rivers at the city-state of Ashur. Under the leadership of Shamshi-Adad the Assyrians tried to create their own empire, but they were squashed by the Babylonian king, Hammurabi. Then the Asiatic Hurrians (Mitanni) invaded, but they were, in turn, overcome by the growing Hittite Empire. The Hittites gave up control of Ashur because it was too far away; thereby granting the Assyrians their long sought independence (c. 1400 B.C.).
The Assyrians didn't just want independence, though. They wanted control and so, under their leader Tukulti-Ninurta (c. 1233-c. 1197 B.C.), known in legend as Ninus, the Assyrians set out to conquer Babylonia. Under their ruler Tiglat-Pileser (1116-1090), the Assyrians extended their empire into Syria and Armenia. Between 883 and 824, under Ashurnazirpal II (883-859 B.C.) and Shalmeneser III (858-824 B.C.) the Assyrians conquered all of Syria and Armenia, Palestine, Babylon and southern Mesopotamia. At its greatest extent, the Assyrian empire extended to the Mediterranean Sea from the western part of modern Iran, including Anatolia, and southward to the Nile delta.
For the sake of control, the Assyrians forced their conquered subjects into exile, including the Hebrews who were exiled to Babylon.
The Assyrians were right to be fearful of the Babylonians because, in the end, the Babylonians with help from the Medes, destroyed the Assyrian Empire and burned Ninevah.
Babylon was a problem having nothing to do with the Jewish diaspora, since it resisted Assyrian rule. Tukulti-Ninurta destroyed the city and set up an Assyrian capital at Ninevah where the last great Assyrian monarch, Ashurbanipal, later established his great library. But then, out of religious fear (because Babylon was Marduk's territory), the Assyrians rebuilt Babylon.
What happened to Ashurbanipal's great library? Because the books were clay, 30,000 fire-hardened tablets remain today providing a wealth of information on Mesopotamian culture, myth, and literature.For information on Mesopotamia, see the first of the series of Near East Introductory articles -- Sumer
For information on Hammurabi, Marduk, and Babylonia, see the second of the series of Near East Introductory articles -- Babylonia