In 438 CE the Empress of the Western Roman Empire, Eudoxia, removed the ban on Jews praying at the Western Wall of the former Temple, signalling an end to the period of rampant persecution. Seven years later when her emperor husband was murdered, she summoned an African king to invade and carry her away from an undesirable second marriage; just like her sister-in-law had done when she invited Attila the Gun and his elephants.
Roughly 2,500 years ago (597 BCE) when Jerusalem was overthrown by the Biblical king of the Chaldeans, Nebuchadnezzar, he deported 10,000 of the best trained and educated Israelites to the capital city of his empire, Babylon. Historically, this was one of the more bloodless tactics for preventing revolt in a conquered people and a typical Mesopotamian practice. In 586 BCE, a Babylonian conquest sent most of Jerusalem into exile. Today the ruins of Babylon are southwest of Baghdad in Iraq.
During the period of late antiquity (3rd to 5th centuries CE) Jews in Babylon were largely completing the Talmud there at the Sura Academy. After the destruction of the Second Temple in Jerusalem in 70 AD, Babylon increasingly became the world center of Jewish scholarship. The Jerusalem Talmud work was interrupted by Roman conquest and persecution, and resumed in Babylon in roughly 375 CE.
Most of the scholarship was performed by two sages, Rav Ashi and Ravina over the next century, although the Talmud would be added to until about 700 CE. Jewish people lived in this region under Chaldean, Persian, Greek, Parthian, and Muslim rule for more than 2,300 years mostly in peace with their neighbors. The Chaldeans were Zoroastrians, but saw the Hebrews as a bulwark against Roman Christiandom, and so did not forcibly convert them.
It would not be until the poison of Nazism took root in the Middle East that Israelites or Jews were cast out of Babylon or Iraq.