Christianity of course began as a sect of Judaism, with Jesus and his original apostles all Jews. The first gentiles (non Jews) to become Christians were in the 40s and 50s AD, inspired by the apostle Paul. When the Romans crushed the Jewish uprising of 70, destroying the Temple in Jerusalem and taking over direct rule of Palestine, rather than letting it be a Jewish client state, both Jews and Christians fled to other parts of the Empire.
Many Jews ended up in western Europe, where they functioned as a more-or-less tolerated minority for most of the early Middle Ages. Although Judaism had originally celebrated the pastoral life (wandering with one's herds of sheep and goats), almost all of Europe's Jews were city-dwellers.
They were especially active as merchants and money-lenders. The Old Testament forbids charging interest ("usury") to one's "brothers," but Jews and Christians decided they were not each other's brothers, so it was all right. All commercial enterprises require access to credit, so they were needed. Many major banking houses throughout the Middle Ages were run by Jews.
And yet Jews also faced intermittent discrimination. Medieval theologians called Jews "Christ-killers" (a position, interestingly, which the modern Catholic church has rejected). When faced with discrimination, Jews would move on, from the Mediterranean regions where they remained most numerous into Germany.
Real attacks on Jews began at the end of the eleventh century. At exactly this time Europeans were also beginning to worry much more about heresy and to find it offensive that the Holy Land was ruled by non-Christians (Muslims). When the First Crusade was launched in 1095, some knights decided to get a head-start on killing "enemies of Christ" by attacking Jews in the cities of the German Rhineland.
Some were horribly slaughtered. In other cases, however, the merchants, even the bishops, stepped in to protect the Jewish populations of their cities, and Christians hid their Jewish neighbors. But from then on, attacks on Jewish communities became more frequent. Again, persecuted Jews found it easiest to just move on. Most of the important rituals and holidays of Judaism are practiced in the home, with the family, so it was easier to keep the traditions alive than if they had required organized churches.
Stories sprang up in the twelfth and thirteenth centuries that Jews killed Christian babies and used their blood for secret incantations. If a well went bad, it was easy to accuse the Jews of poisoning it. Jewish communities kept moving from western Germany, off into the thinly populated stretches of eastern Europe. Many Jews from what had been a major Jewish intellectual and merchant center of Speyer (in Germany) ended up in the Russia/Poland area and were referred to as Shapiro (guy from Speyer). Here in eastern Europe Yiddish developed, a mix of German and Hebrew and some terms from the local Slavic languages.
By the late Middle Ages Jewish communities were more and more frequently persecuted. Several of Europe's kings took out massive loans from the Jews and then drove them out of the country, so as not to have to repay. In 1492, Ferdinand and Isabelle of Spain drove both Jews and Muslims out of Spain. Many went to what is now Turkey, where the Muslim rulers who had recently taken over the last of the Byzantine empire were happy to welcome them. Others "officially" converted to Christianity but continued their Jewish rituals at home, rituals continued long after their descendants forgot that they had ever been anything but Christian. (Click here for more on Ferdinand and Isabelle.)
The Jews are designated a Chosen People in the Bible. Between the Babylonians, the Romans, medieval discrimination, later pograms, and eventually the Nazis, they may (to repeat an old joke) have often wished God would choose somebody else for a change.