For a long time, it was generally accepted that Europeans were direct descendants of Palaeolithic settlers of the continent, with some Middle Eastern ancestry in the Mediterranean regions, courtesy of Neolithic farmers. However, in the last few years, largely thanks to ancient DNA results, it dawned on most people that such a scenario was unrealistic. It now seems that Europe was populated after the Ice Age in a big way, by multiple waves of migrants from almost all directions, but especially from the southeast.

via Eurogenes Blog: Southwest Eurasians + Northwest Eurasians + Mesolithic survivors = modern Europeans.