Neanderthals almost certainly did not interbreed with Homo sapiens.

In light of recent advances in genetics, the general consensus in the scientific community is that the neanderthals were an entirely separate species that did not interbreed with anatomically modern man (Homo sapiens sapiens). This consensus is based on recent studies of mitochondrial DNA.

Mitochondrial DNA is a type of DNA found in the mitochondria of cells. This DNA is carried on the X chromosome and thus is inherited by every person from his or her mother. More importantly, this DNA does not mix with any DNA from the chromosome from the father and thus remains constant within a given family, except for random mutation. Because DNA mutates at a relatively constant rate, mitochondrial DNA samples taken from two different people can be used to date how long ago those two people had a common ancestor.

Mitochondrial DNA taken from people all over the world has shown that human beings had a common ancestor who lived in Africa about 150,000 to 100,000 years ago. Studies of Neanderthal DNA, however, suggest that Neanderthals had a common ancestor at least 250,000 years ago. Thus, we know that there can not have been any interbreeding between the ancestors of present day humans and Neanderthals because in that case, the date derived from human mitochondral DNA would have to have at least as old as that of Neanderthals. Although we have strong evidence that both Neanderthals and Homo sapiens were living side by side in Europe about 35,000 years ago, we can be virtually certain that the Neanderthals were an entirely separate species - H. neanderthalensis - rather than a subspecies (H. sapiens neanderthalensis).