And, what happened to the Neanderthals? What happened to those hairy-backs that once roamed across northern Europe?

They were morphed into Turks and Germans. Thus if your DNA shows traces of Germanic or Turkish heritage you are part Neanderthal. This is my theory and as evidence, I offer a history of barbaric, anti-social behavior of both Turks and Germans.
This history is readily available on the WWW.

At first the Neanderthals were heralded as the ancestors of modern Europeans. As evidence of their intellectual superiority they submitted the large cranium of the Neanderthal. Here was their proof of more superior evolution than that of Black Africans. Solidifying the theory, at least for them, that Africa was civilized by an external source. They even went as far as to fake evidence. (http://www.google.com/search?hl=en&lr=&q=Fossil+Frauds&btnG=Search)

With the genetic proof that modern humans (homo-sapiens-sapiens) originated in Africa, something had to be done with these brutes. At first they claimed that the Neanderthals became extinct during the last ice age, but, the appearance of post Ice Age fossils proved problematic. What were they to do?

At present there is a public relations campaign to replace the unflattering opinion held by most about the behavior and culture of the Neanderthals. I am sure you have heard recently that evidence has been found of a reverence for their dead. One program went to great lengths to prove the size similarity between the brains of Neanderthals and modern humans.

All this, I believe, is leading up to the final revelation that indeed modern Europeans, Indo-Europeans and some Asians are in varying degrees, descended from Neanderthals.

With the advent of the ice age animals would have instinctively moved south to warmer climates. If, as scientists have claimed (the natives claim they have always been here), native Americans followed their prey across the Bering Strait, what prevented the Neanderthals from following their prey south?
Fossil evidence has been found to prove the presence of Neanderthals in the Sinai Mountains.

It is easy to imagine the miscegenation process now underway in western Sudan taking place on a smaller scale as the stronger and brutish, Neanderthal moved in on the territory of modern humans. The majority of them probably got no further than Turkey and other parts of western Asia, but some more adventurous, undoubtedly infiltrated Arabia, Syria and Lebanon. It would have been easy to overcome the sprinkling of male modern humans and capture their women. With the probability of female survivors decreasing the further they traveled, male Neanderthals would have been in serious need of some female company.
Thus we have our "Out of Africa" Eve and an explanation for the genetic differences found in the Y-chromosomes of non-African males, particularly western Asian and Caucasian males.