Under the Persians the Jews did very well. They were able to worship their own God, and even to travel around the Persian Empire converting people to Judaism. But in 331 BC Alexander the Great, who was from Macedon, conquered the Persian Empire and "liberated" (as he called it) the Jews from Persian rule. At first the Jews thought that they would be independent again and have a king, but it soon turned out that Alexander was making Israel part of his own empire. After Alexander died in 323 BC, Israel became part of the empire of Alexander's general Seleucus.
In 168 BC, the Seleucid king Antiochus IV tried to make the Jews worship the Greek gods instead of their own. He sacrificed a cow to Zeus on the altar in the Temple. The Jews were very upset and, led by the Maccabee family, they revolted and gained their independence from the Seleucids. Our holiday of Hanukkah comes from this rebellion. The Jews set up a new independent state of Israel.
Bibliography and further reading about this period of Jewish history, check out this book from Amazon or at your local library:
Heritage and Hellenism: The Reinvention of Jewish Tradition (Hellenistic Culture and Society) by Erich S. Gruen