We know that Neanderthals and early Homo Sapiens (i.e., us humans) overlapped for tens of thousands of years. Neanderthals existed for about one hundred thousand years before going extinct, and the bulk of the evidence suggests they did not interbreed with us, though we did share a common ancestor. They were our distant cousins.
There must have been some critical difference that let us flourish but killed them off, but no one knows for sure what that difference is. We both used sophisticated tools, hunted animals, built shelters, buried our dead, sang and talked, and wore clothes.