What it was. Assyria takes its name from its first capital, the city of Asshur on the western bank of the Tigris; its great later capital was Nineveh, opposite modern Mosul (ISBE, "Assyria," I–II). The ISBE describes a hard, military state: where Babylonia to the south was a temple-centered theocracy with the king under the priest, in Assyria "the royal palace dominated everything" and the king himself was supreme, both commander of the army and chief priest of the national war-god Asur (ISBE, "Assyria," X–XI). The army was the instrument of the state: cavalry, infantry, bowmen and slingers, a corps of charioteers, and an engineering train of battering-rams and siege-works that made it, in the ISBE's phrase, "an irresistible engine of war." Isaiah's image of Assyria as "the rod of mine anger" and Nahum's taunt over Nineveh's fall both assume exactly this terror (Isaiah 10:5; Nahum 2–3).
How it dealt with Israel and Judah. Assyria became the dominant power of western Asia under Tiglath-pileser III (745 BC) and stayed so for over a century. Its signature policy was mass deportation, uprooting a conquered people and resettling them far away to break the will to revolt; this is the machinery behind the exile of the northern kingdom. The ISBE traces the contact: Shalmaneser II had already, in the 9th century, taken tribute from "Jehu son of Omri" (shown on the Black Obelisk) and fought "Ahab of Israel" at Qarqar in 853 BC (the ISBE’s own reckoning gives 854, following a different recension of the Assyrian eponym list); from Tiglath-pileser III onward the small kingdoms were swallowed one by one, Galilee annexed, Damascus destroyed, Samaria besieged and finally carried into captivity in 722 BC (2 Kings 15–17; ISBE, "Assyria," XIV.3). Judah survived as a vassal, paid for with the temple treasury.
Its end. Assyria's power broke as quickly as it had risen. Exhausted by Ashurbanipal's wars, it could not hold off the Medes and the resurgent Babylonians; Nineveh was destroyed in 612 BC and never reinhabited, and the last king fell a few years later (ISBE, "Assyria," XIV.4). The prophets had foretold exactly this collapse of the empire that had seemed unstoppable (Nahum; Zephaniah 2:13). (Source: ISBE 1915, "Assyria"; underlying monuments named in the ISBE include the Black Obelisk of Shalmaneser and the palace excavations of Layard at Nimrud/Nineveh.)