The Roman conquest of Israel and Egypt in the last century BC brought many Jews into the Roman Empire (though many Jews lived in Babylon or elsewhere in the Parthian Empire as well). Many stayed in Israel, but others moved to Rome or other parts of the Roman Empire. Because they had a different religion and a different way of life, and because they refused to worship the Roman Emperor as a god, the Romans treated the Jews with some suspicion.
But the Romans, like the Persians, did allow the Jews to keep on practicing their religion. The Roman Emperor Caligula had an anti-Jewish policy, and in 40 AD tried to put his own statue in the great Jewish Temple in Jerusalem, but when there were riots about this by the Jews in Alexandria, in Egypt, Caligula’s successor Claudius allowed the Jews to practice their religion.
By 66 AD, however, in the reign of the Roman Emperor Nero, the Jews decided to revolt against Rome as they had under the Maccabees and try to get their independence back. Nero sent one of his minor generals, the future emperor Vespasian, to put down the revolt. When Vespasian became emperor in 69 AD, he left his son Titus to finish off the Jewish revolt.
Titus fought the Jews until he won. One of the last holdouts was the fortress of Masada, where a last group of Jews held out until the Romans built a great ramp up to the fortress and broke down the walls (the story that all the Jews then committed suicide is probably not true).
When Titus returned to Rome, his brother Domitian built a great big stone triumphal arch in his honor, and inside it there are carvings showing Titus carrying away the sacred things of the Jews, including a menorah.
Titus also, in 70 AD, destroyed the Second Temple of the Jews in Jerusalem, which has still not been rebuilt. Thanks to the Jewish writer Josephus, who wrote a history of the revolt, we know a lot about it.