Most people today carry around at least a trace of Neanderthal DNA, the legacy of reproduction between Homo sapiens and Homo neanderthalensis thousands of years ago. Genetic studies show that such interbreeding happened time and again in different populations, and although we don't know the circumstances, we might assume that a variety of circumstances were involved over time. An article at BBC Future begins with a scenario taken from romance novels, but soon gets into the science of Neanderthal-modern human relations, like a study of Neanderthal dental plaque. Anthropologist Laura Weyrich discovered the common oral microbe Methanobrevibacter oralis, but this sample was the human version, not the variety that normally inhabited Neanderthal mouths.
Weyrich explains that one possible route for the transfer is kissing. "When you kiss someone, oral microbes will go back and forth between your mouths," she says. "It could have happened once but then sort of been somehow magically propagated, if it happened that the group of people who were infected went on to be very successful. But it could also be something that occurred more regularly."
Another way to transfer your oral microbes is by sharing food. And although there is no direct evidence of a Neanderthal preparing a meal for an early modern human, a romantic meal could have been an alternative source of M. oralis.
Such studies also give us insight into Neanderthal-human transfer of sex-linked chromosomes, cancer, STDs, and immune systems. This much sharing may eventually lead us to conclude that modern humans didn't wipe out the Neanderthals so much as we just absorbed them.