Assyria has a long history, and the political-empire relates to the Bible in a variety of ways.
First of all, Genesis 10:10-12 describes the founding of four Assyria cities by the legendary Nimrud. After this, Assyrian documents (and Hittite treaties) might influence the composition of the Book of Deuteronomy, for we see plenty of covenant-parallels between the two forms.
Eventually, the Neo-Assyrian Empire rises, overtakes Israel (but not Judah) and influences some major books in biblical history, particularly Isaiah, Kings, Jonah, Joel and Chronicles.
Captivities begin between 740 and 732 B.C., with the Assyrians hauling off people from the Northern Kingdom (Samaria), yet sparing the Southern Kingdom (Judah) for a little while longer. Samaria finally falls for good in 722 B.C., never to recover.
According to 2 Chronicles 30, written much later in history than the Book of Kings, at least some Northerners survived and stayed, but not many–being invited by the Southern King (Hezekiah) to attend annual festivals with the Judean Kingdom.
One Assyrian Cuneiform tablet tells of approximately 27,000 people from Samaria were taken by Sargon (Luckenbill, Daniel David. Ancient Records of Assyria and Babylon, Oriental Institute University of Chicago, Chicago, Illinois, 1926. ISBN 1-85417-049-X), which would not be as many as calculated by some–often numbering in the hundreds of thousands. This discrepancy probability tells us that many of them fled to the Southern Kingdom (sharers of their cultural heritage).
Called by their tribal names, some people from ‘Ephraim and Manasseh’ survived the Assyrian deportation and even seem to have remained in their own lands (2 Chron. 30:1). 2 Esdras 13:40-48 (an Apocryphal text), imagines them completely swept away, yet with little specificity (one has to account for rhetorical poetics, especially by an event written much later than the happenings).
Eventually, in the New Testament, whenever Isaiah, Jonah or often Kings is called upon (to compare to the events of the past to newer times. involving the Romans and Jesus), the Assyrian political-situation hovers in the background. Event though such events happened seven or eight-hundred years before Christ was born, the Gospels use verses from the Israeli-Assyrian past to make sense of the happenings in the historical ‘present’ (that which was contemporary to the Gospel-writers).
If you don’t know Assyria, you won’t know the Christmas story as well as you could (cf. Isaiah 9, particularly Isa. 9:6-7).