Middle Eastern refugees killed off Neanderthals 40,000 years ago. Look it up.
Actually, according to this one thing I recently came across it may have been a volcanic eruption.
Essentially, Neanderthals, as rugged as they were, required a lot of calories and the majority their territory fell within the ash fall out of this one big blow. Where they were out from under the effects of the volcano, along the west coast of Europe, they persisted longer.
There is nothing like that to look up. No one is really sure how, why, or even when the Neanderthal disappeared. The last known finds date to 28,000 ya.
The most modern theory is that they didn’t ‘disappear’, but were blended into the current human race - but that’s a theory not a fact. However, there are Neanderthal genes present in modern humans.