The Khazar hypothesis is an argument that Ashkenazi Jews (i.e., those descended from a German bloodline) are not ethnically Jews, but descended from the Turkic Khazar Empire. This myth is often harnessed in attempts to discredit Zionism and/or to explain why the British/Aryan/insert race here are the REAL chosen people of the Bible, and not the Jews.
 The Khazar state
The Khazar state, at various times referred to as the Khazar Khaganate or Khazaria, was a Central Asian polity in the medieval era. Many Jews sought refuge from turmoil in Persia and the Byzantine Empire in the Khazar region, and by the 10th century, it is estimated that there were about thirty thousand Jews living in Khazaria. Around the 8th century, the Khazars' ruling class converted to Judaism, and from then on they cultivated relations with diasporic Jewish communities across Europe and Asia until their fall in the 10th century.
 The Thirteenth Tribe
The Thirteenth Tribe is a book by Arthur Koestler, claiming that Ashkenazi Jews were descended from Khazar converts to Judaism. The author apparently had the best of intentions, and thought that by establishing Khazar descendence, anti-Semitism would disappear.
 Genetic studies
Many argue that genetic studies on Jewish populations have refuted any claims of significant Khazar lineage, and have shown that most ethnic Jews draw their roots from the Middle East.A genetic study led by Gil Atzmon found that European Jews were most closely related to Middle-Eastern Jews, Palestinians, Druze, and non-Jewish Southern Europeans - evidence inconsistent with Khazar/Slavic hypotheses. Another genetic study led by Doron Behar found that, despite admixture from local populations, autosomal genetic samples from the Ashkenazi Jews, Caucasian Jews, Middle Eastern Jews, North African Jews, and Sephardi Jews form a relatively tight genetic cluster which overlaps with Samaritans and Israeli Druze which is strongly indicative of common Levantine ancestry
This argument has been challenged by one recent genetic study by Johns Hopkins University geneticist Dr. Eran Elhaik. However, Elhaik’s study does not fully address the findings of previous studies, particularly the overlap between Ashkenazi Jewish populations and native endogamous Levantine populations such as the Samaritans and Druze. Elhaik’s use of Palestinian Arabs as representative of ancestral Israelite genetics is questionable in light of previous genetic studies which have uncovered evidence of significant African gene flow present in Arab, but not non-Arab Middle-Eastern populations. Blogger Razib Khan argues Elhaik’s conclusions rely on poorly reasoned assumptions and that “the Caucasian component that is being detected in this paper may simply be a indigenous Middle Eastern ancestral element which has now been somewhat displaced northward in its modal frequency due to the expansion of the Arabs.” 
None of these studies of Ashkenazi Jews have detected evidence of a significant Central or East Asian genetic component which is present in other Turkic populations. The actual Khazars would likely have been assimilated by the Krymchaks (Crimean Jews) following the fall of the Khazars. Even so, the Krymchaks had a long history of assimilating other Jews who came to the Crimea, so their ancestry is still largely Levantine. 
 Why it wouldn't matter anyhow
Though Ashkenazi Jews are the largest ethnic group of Jews today, Sephardim (Jews of Spanish & North African descent) and Mizrahim (Jews of Middle Eastern descent) make up a nontrivial part of the Jewish population, both in Israel and in the diaspora. Furthermore, Israel has become the home of many smaller Jewish ethnic groups, such as Ethiopian Jews, Yemenite Jews, and Kaifeng Jews. Since the Khazar myth doesn't address those Jews at all, any use of it to prove that "the Jews" aren't real Jews has significant holes.
Furthermore, Judaism has allowed for voluntary conversion through most of its history. Indeed, the great-grandmother of King David, Ruth, was a Moabite convert. Therefore, even if the Ashkenazi were descendants of Khazar converts, they would still be entirely, legitimately Jewish in the eyes of Jewish law.
Additionally there is the question of gene mixing which would inevitably occur when two populations lived close together. No matter how stringent social or religious constraints might be against either mixed marriages or extramarital sex it's still going to happen.
- ↑ AN INTRODUCTION TO THE HISTORY OF KHAZARIA, Kevin Alan Brook
- ↑ Michael Scammell Koestler: The Literary and Political Odyssey of a Twentieth-Century Skeptic Random House, 2009, p. 546
- ↑ Jews: A religious group, people or race? Judy Siegel-Itzkovich
- ↑ Atzmon, Gil, Li Hao, Itsik Pe’er, Christopher Velez, Alexander Pearlman, Pier Francesco Palamara, Bernice Morrow, Eitan Friedman, Carole Oddoux, Edward Burns, and Harry Ostrer. 2010. “Abraham’s Children in the Genome Era: Major Jewish Diaspora Populations Comprise Distinct Genetic Clusters with Shared Middle Eastern Ancestry”. The American Journal of Human Genetics, 86: 850–859.
- ↑ Behar, Doron M, Bayazit Yunusbayev, Mait Metspalu, Ene Metspalu, Saharon Rosset, Jüri Parik, Siiri Rootsi, Gyaneshwer Chaubey, Ildus Kutuev, Guennady Yudkovsky, Elza K. Khusnutdinova, Oleg Balanovsky, Ornella Semino, Luisa Pereira, David Comas, David Gurwitz, Batsheva Bonne-Tamir, Tudor Parfitt, Michael F. Hammer, Karl Skorecki1, and Richard Villems. 2010. “The genome-wide structure of the Jewish people”. Nature, 466: 238–242.
- ↑ 
- ↑ 
- ↑ Moorjani P, Patterson N, Hirschhorn JN, Keinan A, Hao L, et al. (2011) “The History of African Gene Flow into Southern Europeans, Levantines, and Jews”. http://www.plosgenetics.org/article/...l.pgen.1001373
- ↑ Martin Richards,Chiara Rengo, Fulvio Cruciani, Fiona Gratrix, et al. (2003) “Extensive Female-Mediated Gene Flow from Sub-Saharan Africa into Near Eastern Arab Populations” http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1180338/
- ↑ “Ashkenazi Jews are probably not descended from the Khazars” http://blogs.discovermagazine.com/gnxp/2012/08/ashkenazi-jews-are-probably-not-descended-from-the-khazars/#.UWi7nKJg-jN
- ↑ "Who Were The Krymchaks?" http://www.family.askinazy.com/WhoWereTheKrymchaks.pdf
ref> “Ashkenazi Jews are probably not descended from the Khazars” http://blogs.discovermagazine.com/gnxp/2012/08/ashkenazi-jews-are-probably-not-descended-from-the-khazars/#.UWi7nKJg-jN