First, the recent research. A team led by Harry Ostrer of New York University studied the DNA of 237 Jewish people from seven regions of the world and compared that DNA with the DNA of 418 non-Jewish people from the same regions. All the Jews in the study had four grandparents from the same region. Ostrer and his colleagues found that the Jews from different regions were more closely related to each other than to the general non-Jewish population in their region. Additionally, they found that Iranian and Iraqi Jews are descended from Persian and Babylonian communities of the fourth through sixth centuries BCE; no surprises there. Finally, they found that European Jews diverged from Middle-Eastern Jews beginning some time during the first millennium BCE.
There is more. The closest non-Jewish relatives of Iranian, Iraqi, and Syrian Jews, for example, are Druze, Bedouins, and Palestinians. Again, no surprises. In addition, we have known for years that European Jews, at least, have genetic links to the Middle East. Related research by Michael Hammer of the University of Arizona examined the Y-chromosomes of Jewish men who identified themselves as Cohanim (the priestly caste) and found over a decade ago that the vast majority had a common ancestor who lived in early Biblical times.
Now the Khazars. Some time between perhaps 750 and 850 CE, the Khazar kingdom on the Caspian Sea and along the Volga River supposedly converted to Judaism, though it is unclear whether that means the nobility or the general population. The history of the Khazar kingdom is also unclear, at least to me, but by 1000 CE the kingdom had been destroyed by the Vikings. In 1976, the novelist and essayist Arthur Koestler published The Thirteenth Tribe, a nonfiction work in which he revived and popularized the theory that European Jews were descended from the remnants of the Khazar kingdom and not from the Middle East. Professional historians were not sympathetic, and Ostrer found only limited interbreeding between Jews and Khazars and Slavs.
One of Koestler’s stated intentions in writing the book was to combat anti-Semitism by demonstrating that modern Jews are not the biological descendants of first-century Jews. Koestler said (and I agree) that the Khazar theory ought to have no bearing on modern Israel. He was apparently unaware, however, that anti-Semitic groups had used just that theory to discredit the State of Israel. Most probably, his book did more harm to his cause than good.
Ostrer’s genetic data, fortunately, probably discredit the already weak Khazar theory once and for all.