There's a paleobiologist who is arguing that for modern Europeans to have as much Neanderthal DNA as they currently have the population must have started out as something like 50% Neanderthal.
That would make us the descendants of Neanderthals, meaning they never went extinct but just got bred into a larger population where many of their traits were selected against over time.
I agree. And since we carry their (known) DNA, they are our ancestors, and we’re not (yet) extinct, so yeah. :^)
To my understanding, East Asians have the largest amount of Neanderthal DNA, followed by Europeans, then South Asians etc.