It surprises me that some people still think modern humans (Homo sapiens sapiens) evolved from Neanderthals (Homo sapiens neanderthalensis). Our ancestors and the Neanderthals were two human species that had a common ancestor (probably Homo heidelbergensis). Yes, there was actually a time when there were more than one human species on this planet other than Homo sapiens. Think of it like the situation in Lord of the Rings: Men, Elves, Dwarves, Hobbits, Orcs, etc. were running around the place, each species sentient and capable of interacting with one another on a cultural level. Except that--in the case of Homo sapiens, Neanderthals, and the other human races--we were using stone axes instead of Dwarven axes, living in caves and mud huts instead of palaces and walled cities, and everyone was kinda just grubbing around instead of making magic rings. There is evidence of Cro-Magnons and Neanderthals hunting mammoths together, though; and that's kinda like the Alliance of Men and Elves.
But where did the other human species go? Well, in the case of the Neanderthals, recent evidence indicates that they did not exactly go extinct. They hooked up with the Cro-Mags. They interbred with the Cro-Magnons (early modern humans), resulting in modern humans having 1-4% Neanderthal DNA. That is, except for ancient African Homo sapiens, because they did not leave Africa. There are those who infer that African people are the true Homo sapiens, everyone else is a Homo sapiens-Neanderthal hybrid.
This opens a can of worms on the race debate. White supremacists on Stormfront insist that Neanderthals were the reason for white people and that the lighter your skin, the more Neanderthal DNA you have.
You wanna know something that opens another can of worms? Two words: Denisova hominins. They're Paleolithic Era hominids distinct from Cro-Magnons and Neanderthals. Genetic tests indicate that for many modern Melanesians and Australian Aboriginines, 4-6% of their genome comes from Denisovans. Early modern humans weren't shacking up with just the Neanderthals. They were also doing the dirty cha-cha with the Denisovans.
Prehistoric college parties must have been epic.