With the advent of dense maps of human genetic variation, it is now possible to detect positive natural selection across the human genome. Here we report an analysis of over 3 million polymorphisms from the International HapMap Project Phase 2 (HapMap2). We used ‘long-range haplotype’ methods, which were developed to identify alleles segregating in a population that have undergone recent selection, and we also developed new methods that are based on cross-population comparisons to discover alleles that have swept to near-fixation within a population. The analysis reveals more than 300 strong candidate regions. Focusing on the strongest 22 regions, we develop a heuristic for scrutinizing these regions to identify candidate targets of selection. In a complementary analysis, we identify 26 non-synonymous, coding, single nucleotide polymorphisms showing regional evidence of positive selection. Examination of these candidates highlights three cases in which two genes in a common biological process have apparently undergone positive selection in the same population: LARGE and DMD, both related to infection by the Lassa virus3, in West Africa; SLC24A5 and SLC45A2, both involved in skin pigmentation in Europe; and EDAR and EDA2R, both involved in development of hair follicles, in Asia.