I thought all would depend upon isolating neanderthal nuclear DNA, a thing which may never happen. However, I wasn't reckoning with the ingenuity of the scientists in the field. There's another way. They have found some few genes which a lot of non-Africans have and which Africans don't. These genes may be the heritage of our interbreeding with not-so-related hominids after the last radiation from the breeding ground.
I'm pinging blam because I know he also likes the idea that the neanderthals are still around -- in us.
Not necessarily. This old "non-African" gene could have originated in Africa, but it might have been a local thing, and was mostly concentrated in the tribes that migrated out. The migrants took it with them before it had a chance to spread throughout Africa.