Interesting. I had learned mostly about this stuff in high school and college when the thinking was that Neanderthals were basically the earliest Homo Sapiens and not a seperate species. Science advances . . .
Homo Sapiens and Homo Neanderthalensis both sprang from the earlier Homo Erectus. There is really little evidence that Neanderthals and humans ever interbred, and even that is controversial. DNA analysis indicates the prospect of such a breeding to be nil. They may have been about as closely related to us as donkeys are to horses.
The most interesting thing to come out in recent years (at least to my lights) is that Homo Erectus may possibly have survived up until about 50k years ago. This means that at one time there were three human species sharing the planet at the same time.