Could Homo Sapiens Sapiens and Homo Sapiens Neanderthalis interbreed or not?

[Don'tcallmedude]

I vaguely remember reading about a DNA analysis a few years back that came to the conclusion that the two were too different genetically, and that any crossbreeds would have been infertile, like mules are (from donkeys and horses).

Yet recently there have been many stories in the press about genetic traits found to be in both species, and attributing this to interbreeding.

What's the currently-accepted viewpoint on this among specialists in the field?

Could they interbreed or not, and if so, could crossbreeds reproduce themselves?

If so, does that mean we weren't really different species, just variations within one species?
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[BraveMasai]

The DNA evidence suggests, that we can, and did interbreed.

Though we were separated by 1/4 million years, or so, we share the same evolutionary "grandparent", so to speak, H. erectus.

Neanderthals were likely, a bit more different, genetically, than our current range of races, throughout the world.

However, as far as offspring, being similar to sterile mules, it's not likely, because the hybrids found, would indicate about one-in-a-trillion odds, of finding several sterile hybrid specimens, at a variety of locations throughout Asia and Europe.

What's more likely, is that Neanderthal DNA eventually became dormant or recessive, though it's currently found at the rate of 1-4%, in modern, Non-African Humans!