Jews do not believe in Jesus. And why should they? This is puzzling to many Christians, but to Jews, the question has bitter overtones that recall centuries of pogroms and persecution. It is true that there are messianic Jews who believe in Jesus, but this is anathema to mainstream Judaism. Main-stream Jews still await the arrival of the Messiah.
Jews have formulated many images of the messiah. In the twelfth century, the great scholar, physician, and community leader Maimonides defined the conditions the messiah needs to meet in a formulation that has since become standard in traditional Judaism:
If a king from the House of David studies Torah, busies himself with the commandments like David did, observes the laws of the written and the oral law, convinces Israel to walk in the way of the Torah and to repair its breaches, and fights the battles of the Lord, it may be assumed that he is the Messiah. If he succeeds at these things, rebuilds the Temple on its site, and gathers the dispersed of Israel, he is beyond all doubt the Messiah…But if he does not succeed fully, or is slain, it is obvious that he is not the Messiah promised in the Torah.(Maimonides, Laws of Kings 11:3-4 (version)
To most Jews, Jesus did not fulfill the conditions laid out by Maimonides.
Nineteenth-century scholars were the first to reclaim Jesus as a Jew—an idea that was quite shocking at the time—and many Jews today emphasize the exemplary character of Jesus. Similarly, many Christians now reclaim Jesus the Jew. One of my teachers, Klaus Wengst, describes the role of Jesus through the lens of the Torah here.