By now it's pretty obvious that Homo sapiens and Homo neanderthalensis were hot for each other. The two groups of early humans were not separate species—they were kissing cousins, separated by just a few hundred thousand years of evolution. Now we know they started hooking up far earlier than scientists believed was possible.
The standard narrative about how modern humans met Neanderthals is pretty simple. A group of early humans, possibly Homo erectus, hiked out of Africa over 600,000 years ago and settled all over Europe and the Middle East. Over time, they evolved into Neanderthals, Denisovans, and probably several other groups. Meanwhile, back in Africa, the common ancestor of Neanderthals and Homo sapiens was busily evolving into—you guessed it—Homo sapiens sapiens. Around 70 thousand years ago, modern humans started streaming in huge numbers out of Africa, into Europe and the Middle East, possibly spurred on by chilly weather caused by the Toba eruption in Indonesia. There, they met up with their long-lost cousins and immediately started humping.
Genetic analysis has confirmed that said humping took place. Seems like that should be the end of the story, except that even during the Pleistocene, relationships were complicated.
Making things even more complicated is the fact that recent studies have pushed back the date on the last common ancestor of Neanderthals and modern humans by several hundred thousand years. So we're not sure when the ancestors of Neanderthals split off from modern human ancestors, but it may have been as long ago as 700,000 years.
A new paper published in Nature suggests that we also have to revise our hypotheses about when Neanderthals and Homo sapiens met up again. New genetic analysis of Neanderthal and Denisovan bones found in the Altai mountains, Siberia, reveals that Homo sapiens DNA was already flowing into these populations 100,000 years ago. We don't see this same early influx of modern human DNA in other Neanderthal groups from Spain and Croatia. So the evidence suggests that some Neanderthals came into contact with modern humans long before others did.
Perhaps more importantly, the results of this long-ago hanky panky also help us to understand what the human population was like when modern humans first migrated out of Africa. Evidence has been mounting that early modern humans were living in the Levant and China over 120,000 years ago. This new study corroborates this finding, revealing that at least one group of modern humans made it all the way to the Altai mountains over 100,000 years ago, where they formed families with the local Neanderthals.