Most of the Hittites in the Bible (think Uriah the Hittite, you know, the guy David betrayed to his death to cover up his adultery with Uriah's wife, Bathsheba) are the various Neo-Hittite kingdoms in the areas of modern Lebanon, Syria, and Turkey. They too spoke an Indo-European language, Luwian, but also Aramaic, a Semitic language. These kingdoms disappeared in the Assyrian expansion by the end of the eighth century. Conventional wisdom says there were no more Hittites after that time.
Conventional wisdom is wrong.
1 Maccabees opens with the words:
And it came to pass, after the conquest of Alexander, son of Philip of Macedon, who came from the land of the Hittites (Χεττιμ), and he smote Darius, the king of the Persians and the Medes, and he reigned in his stead, and previously over Greece. (1 Maccabees 1:1)The author of Maccabees identifies those place on the other side of the Mediterranean, not to mention Anatolia, as the land of the Hittites (Χεττιμ). This is also reflected in the Dead Sea Scrolls. In the Commentary on Habakkuk, the enemies of Israel (such as the Chaldeans) are identified as Hittites, which seems to indicate the same thing as it does in Maccabees. Modern scholars have often identified the Hittites of the Habakkuk Commentary as the Romans. It seems, in light of the Septuagint, that the term Hittite could either be a geographic or linguistic designation. Geographically it would be the lands northward and across the sea from Israel. Linguistically it would mean Indo-Europeans.
Thus a notion of Hittites continues at least a millennium after the people that modern scholars recognize as Hittites have disappeared from the scene.