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Genomic studies have shown that Neanderthals interbred with modern humans, and that non-Africans today are the products of this mixture^,. The antiquity of Neanderthal gene flow into modern humans means that genomic regions that derive from Neanderthals in any one human today are usually less than a hundred kilobases in size. However, Neanderthal haplotypes are also distinctive enough that several studies have been able to detect Neanderthal ancestry at specific loci^,,,,,,. We systematically infer Neanderthal haplotypes in the genomes of 1,004 present-day humans. Regions that harbour a high frequency of Neanderthal alleles are enriched for genes affecting keratin filaments, suggesting that Neanderthal alleles may have helped modern humans to adapt to non-African environments. We identify multiple Neanderthal-derived alleles that confer risk for disease, suggesting that Neanderthal alleles continue …