Do modern people have Neanderthal genes?

Yes, modern humans actually have some Neanderthal genes! It is estimated that modern humans who are not of African ancestry have about 2-4% Neanderthal DNA in their genome.

This is because modern humans and Neanderthals interbred when modern humans migrated out of Africa and came into contact with Neanderthals in Europe and Asia. The two species are thought to have interbred for thousands of years, and the genetic material that was exchanged has been passed down through the generations to present-day humans.