Ha’aretz has the details. Reading this and other accounts of this and other studies, it now seems well-established that:
(1) The mainstream Ashkenazic and Mizrahi (“Eastern”) Jewish communities share a genetic heritage tracing back about 2,500 years.
(2) These communities maintained sufficient separation from the local non-Jewish populations that despite vast geographic distances, to this day they have greater genetic similarity with each other than with the non-Jewish population among whom they lived.
(3) The idea that Ashkenazic Jews are primarily descended from converted Khazars, most recently propounded by charlatan Shlomo Sand, is nonsense, and only continues to persist against all scientific evidence because it serves the ideological agendas of anti-Semites and anti-Zionists.
(4) Some isolated Jewish communities, like the Ethiopians, either never had, or eventually lost, their genetic connection to the rest of the Jewish people.
(5) Contrary to popular myth, the group that Jews most resemble genetically is not Palestinian Arabs, but the Druze. Geneticists, in fact, put Jews and Druze into one grouping, and Palestinians, Bedouin, and other Arab populations into another.
As I’ve said before, I don’t think such genetic studies bear any true relevance to modern political controversies (nor would they if they had different results)–since “peoplehood’ is purely a social construct anyway, I don’t see why it matters whether Palestinians or Jews “really” are peoples who have long dwelled in the Land of Israel/Palestine, or just think of themselves that way. The studies are nevertheless interesting on their own terms.
But there are those, like Sand, who spend a good deal of time and energy trying to prove the lack of common Jewish genetic heritage, promoting the Khazar myth, and so on, for political reasons, and go so far as to dismiss contrary genetic evidence as Zionist propaganda. To them, the classic response is appropriate: you’re entitled to your own opinions, but not your own facts.