From this story in the Atlantic:
One of the most compelling -- and enduring -- mysteries in archaeology concerns the rise of early humans and the decline of Neanderthals. For about 250,000 years, Neanderthals lived and evolved, quite successfully, in the area that is now Europe. Somewhere between 45,000 and 35,000 years ago, early humans came along. They proliferated in their new environment, their population increasing tenfold in the 10,000 years after they arrived; Neanderthals declined and finally died away. What happened? What went so wrong for the Neanderthals -- and what went so right for us humans?