I will review some of the population genetic analysis motivated by the sequencing of ancient DNA extracted from Neanderthal and Denisova fossils. The models presented are directed to (1) estimating rates of admixture between extinct archaic populations and the ancestors of some modern human populations, (2) distinguishing between admixture and ancestral population subdivision as an explanation for the greater similarity of Neanderthals and modern non-African populations, (3) detecting evidence of natural selection affecting nucleotide substitutions fixed for the derived state in modern humans and fixed for the ancestral state in Neanderthals and Denisovans, and (4) detecting inbreeding in archaic genomes.