We know that the Magyars originated from Inner Eurasia. They were one of the long line of steppe peoples who conquered and settled central Europe, the Avars being their local predecessors. But unlike the Avars, or the Bulgars or the Huns, the Magyars left a cultural imprint: their language. And yet physically and genetically the current Hungarian population seems to exhibit continuity with their European neighbors (in contrast, Gypsies show evidence of haplotypes normally found in the Indian subcontinent). Dienekes points me to some new data:
Strong differences appear when the ancient Hungarian samples are analyzed according to apparent social status, as judged by grave goods. Commoners show a predominance of mtDNA haplotypes and haplogroups (H, R, T), common in west Eurasia, while high-status individuals, presumably conquering Hungarians, show a more heterogeneous haplogroup distribution, with haplogroups (N1a, X) which are present at very low frequencies in modern worldwide populations and are absent in recent Hungarian and Sekler populations.
In other words, the genesis of the modern Hungarian ethnicity occurred via elite emulation as well as assimilation of the that elite by the substrate. Though the Hungarian language is very unique, most other aspects of their culture reflect the region's assimilation toward Latin Christian norms. Note that mtDNA is normally the weaker signal when it comes to the genetic impact of nomads, who are likely to "pick up" women from the conquered peoples during their travels while their patrilineages remain more or less unbroken.
