In Babylonia there were two great Jewish academies that both lasted an astonishing 800 years. They were the famous yeshivas of Sura and Pumbedita. Both were established in the third century CE, and they led the Jewish people throughout the time of the Mishnah, Gemara, and through the time of the Gaonim. They both lasted until the eleventh century.
Wikipedia, mostly quoting The Jewish Encyclopedia (1906) has a brief biography of the last leader of Pumbedita, Hezekiah Gaon:
Hezekiah was a member of the exilarchal family, son of David, who was son of Zakkai, who was the son of Avraham, who was the son of Nathan, son of David a Rabbi, whose father was Hazub. He was elected to the office of principal after the murder of Hai Gaon*, but was denounced to a fanatical government of the Buyyids, imprisoned, and tortured to death. With him ended his family, with the exception of two sons who escaped to the Iberian Peninsula, where they found a home with Joseph ben Samuel, the son of Samuel ha-Nagid. The death of Hezekiah also ended the line of the Geonim, which began four centuries before (see Hanan of Iskiya), and with it the Academy of Pumbedita.I don't believe that Hai Gaon was murdered - none of his other biographies mention that - but Hezekiah II, who amazingly was both the Exilarch and the Rosh Yeshiva, was murdered by a Shiite caliph, and his murder ended the era of Babylonia/Iraq as a major center of Jewish studies. (Some details listed here are disputed in this book.)
Of course, as we read in the kinot today, Christians were responsible for the deaths of thousands of Jews during the Crusades, but few recall that a Muslim ruler is responsible for the end of the primacy of Babylonian Jewry at around the same time.