the origins of Europeans
There's been debate for many years about where modern Europeans came from. There have been anatomically modern people in Europe for 40,000 years or so, but it's not at all clear whether the current Caucasian peoples are primarily descendents of those folks, or instead are primarily descendents of a more recent wave of migrants, sometime 6000 to 10,000 years ago. I'm not an archaeologist, of course, but I've been interested in this question since college, where it comes up in historical linguistics.
Almost all of the languages of Europe, plus languages like Persian, Armenian, and the Sanskrit-derived languages spoken on the Indian peninsula, are members of the Indo-European family of languages. This suggests that there was once a single language, dubbed Proto-Indo-European, spoken somewhere by some people, dubbed Proto-Indo-Europeans. We know that that language spread and diverged over a number of millennia, replacing the other languages spoken in Europe (except Hungarian, Finnish and Basque). Based on linguistic evidence alone, however, there's no way to determine if the Indo-European-speaking people moved, or just the language, or some combination thereof.
There's been lots of speculation, combining the linguistic evidence with the archaeological evidence, but it's not been totally convincing. One of the more prominent arguments (which I wrote a term paper on, if I recall!) is from a British researcher named (Lord) Colin Renfrew (pictured!), who observed that the development of agriculture seemed to coincide with a migration around 9000 years ago, from what is now Turkey into Europe, and suggested that these people were the Indo-Europeans, and that they by-and-large peacefully replaced the hunter-gatherers who were there before. Another, older theory suggests that the Indo-Europeans were a group from the steppes of southern Russian and Ukraine who had domesticated the horse (it's known that Proto-Indo-European, the language, had words for domesticated horses), and who basically invaded Europe about 5000 years ago.
There's some new evidence that seems to support this latter view of events, although it's somewhat hard to draw firm conclusions. The new evidence is based on analyzing DNA. Some earlier work had shown that more than 80% of the mitochondrial DNA in modern Europeans is unique and old, suggesting that modern Europeans are in fact primarily the descendents of the pre-agricultural peoples who lived there before the advent of farming. The new work looks at DNA extracted from the bones of ancient Europeans, those who lived about 7000 years ago or so (and were farmers, based on artifacts found where they were buried). Of 24 individuals studied, they found that 6 had a DNA variation that is now extremely rare. This evidence, combined with the earlier DNA research, seems to suggest that the spread of agriculture did not involve the replacement of the people who were originally there, but that those people were eventually replaced anyway by a fairly coherent group.
Perhaps these people were invaders on horseback, or perhaps they were someone else. So far, there's no real way to tell. No doubt further DNA analysis will help clear up the archeological story. With a little luck, it'll inform the highly speculative linguistic story as well, although I'm waiting for our friends over in Physics to develop a time machine so we can get the real answers...