Does Jesus require his followers to keep the Law? It would seem so: 5:19 states that "anyone who relaxes one of the least of these commandments and teaches others to do the same will be called least in the Kingdom of Heaven". Jesus appears to uphold the authority of the Law, and is clear that nothing can be taken away from it. In many of the antitheses he appears to be arguing against a false or shallow interpretation of the Law rather than the letter of the Law itself. Is Jesus, perhaps, a Jewish Reformer, come to restore the proper reading and practice of the Law by destroying false interpretations?
The answer must be that neither of the above is quite right. We need to read the Sermon as part of the Matthew's gospel, and the big point of Matthew's gospel is that Jesus fulfills the OT. He fulfills it in all sorts of ways: the gospel contains allusions to Moses (40 days and nights of fasting, 4:1), Elijah (multiplying food, 14:13f), the Exodus (2:15 amongst many others), Sinai (17:1-13, which also has echoes of Daniel's Son of Man), David (21:1f) and many others. Not all the allusions are precise, and they are not usually meant to be read in simplistic terms, like "Jesus is the new Moses/David/Israel" etc. Rather, by scattering a wide variety of allusions to Israel's history throughout his gospel Matthew makes the big picture claim that Jesus is the climax of the history of Israel, and the beginning of a new Israel - an Israel which begins with the salvation of the remnant of old Israel - gathered around himself.
And here in the Sermon we find Jesus saying "do not think that I have come to abolish the Law and the Prophets; I have not come to abolish them but to fulfill them" (5:17). The Law is, as far as Matthew is concerned (and Matthew could surely only have got this idea from Jesus), on a par with the Prophets. Both are fulfilled in him. He is the climax of everything they were about, the one who brings them to their intended end - in the teleological sense. Does the law pass away? No more than the prophets pass away! But both have reached that point in their existence where they can be, if you like, tied off. This is the conclusion. Henceforth, it is not the Law that defines our ethics, any more than it is the Prophets who define our expectation. It is Christ, and the Law and the Prophets as they reach their climax in him.