Neanderthals once populated the entire European continent. Around 45,000 years ago, Homo neanderthalensis was the predominant human species in Europe. They reached their population peak right before their population rapidly declined and they eventually became extinct.
Or so it was thought until recently.
Precisely why this species will finally die out for good is still unclear. Perhaps it will be due to low genetic diversity, perhaps to the rise of Homo sapiens like the rest of us with real brains. This question will continue to occupy amateur scientists like myself for some time to come.