The debate over the ethnogenesis of Ashkenazi Jewry is longstanding, and has been hampered by a lack of Jewish historiographical work between the Biblical and the early Modern eras. Most historians, as well as geneticists, situate them as the descendants of Israelite tribes whose presence in Europe is owed to deportations during the Roman conquest of Palestine, as well as migration from Babylonia, and eventual settlement along the Rhine. By contrast, a few historians and other writers, most famously Arthur Koestler, have looked to migrations following the decline of the little-understood Medieval Jewish kingdom of Khazaria as the main source for Ashkenazi Jewry. A recent study of genetic variation in southeastern European populations (Elhaik 2012) also proposed a Khazarian origin for Ashkenazi Jews, eliciting considerable criticism from other scholars investigating Jewish ancestry who favor a Near Eastern origin of Ashkenazi populations. This paper re-examines the genetic data and analytical approaches used in these studies of Jewish ancestry, and situates them in the context of historical, linguistic, and archaeological evidence from the Caucasus, Europe and the Near East. Based on this reanalysis, it appears not only that the Khazar Hypothesis per se is without serious merit, but also the veracity of the Rhineland Hypothesis may also be questionable.