Anatomically modern humans overlapped and mated with Neandertals such that non-African humans inherit similar to 1 to 3% of their genomes from Neandertal ancestors. We identified Neandertal lineages that persist in the DNA of modern humans, in whole-genome sequences from 379 European and 286 East Asian individuals, recovering more than 15 gigabases of introgressed sequence that spans similar to 20% of the Neandertal genome (false discovery rate = 5%). Analyses of surviving archaic lineages suggest that there were fitness costs to hybridization, admixture occurred both before and after divergence of non-African modern humans, and Neandertals were a source of adaptive variation for loci involved in skin phenotypes. Our results provide a new avenue for paleogenomics studies, allowing substantial amounts of population-level DNA sequence information to be obtained from extinct groups, even in the absence of fossilized remains.