Modern humans may have inherited some Neanderthal genes

I know virtually nothing about this subject, and I will try very hard to avoid odious comparisons between Neanderthals and anyone else, but it appears that white and Asian people, but not sub-Saharan Africans, have 1-4% Neanderthal genes in our genomes. You may read news articles about it in the New York Times free or in Science with a subscription. Science also has provided a special feature on the Neanderthal genome and has made two technical articles available without charge, but not the news article cited above. This paragraph has almost completely exhausted my knowledge of the Neanderthal genome.