For Judaism, Babylonia is first a catastrophe and then, for a much longer period, a home.
Jerusalem fell in 587 BCE, the temple was burned and part of the population was deported to Babylonia. The exile lasted about fifty years before a Persian conquest allowed a return, and what happened during it was decisive for the religion that emerged: a community without a temple, sacrifices or a king had to work out what its obligations now were, and the answers, an emphasis on sabbath and circumcision, the assembling and editing of texts, and a theology in which defeat is explained as covenant failure rather than as the defeat of a god, are visible throughout the later books.
Not everyone returned. A Jewish population remained in Babylonia continuously for well over two thousand years, and from roughly the third century CE its academies at Sura and Pumbedita became the leading centres of rabbinic learning anywhere. The Babylonian Talmud, compiled there over several centuries, became the authoritative text of rabbinic Judaism, more so than the earlier Talmud produced in Galilee, and the heads of those academies exercised legal authority over communities across the Islamic world.
The Jewish community of Iraq, direct heir to all of this, was very largely dissolved between 1948 and the early 1950s, when the great majority emigrated to Israel. Almost none remain.