Russian Jews

It just occurred to me that there have historically been a huge number of Russian (and Eastern European) Jews, but after considering it, I haven't the foggiest idea where they came from. The Jewish Diaspora through the Roman and Persian worlds wouldn't have extended to lands beyond those two empires. I know there was at least one major Turkish group that converted to Judaism in medieval times (the Khazars), but I vaguely recall reading a refutation of the idea that Russian Jews were descended from these groups. So how did so many Jews wind up in the belt from Berlin to the Caspian? I know my readers include several Jewish history types. Was there some eastern migration of West European Jews at some point or something?