The past fifty years have seen the development and application of numerous statistical methods to identify genomic regions that appear to be shaped by natural selection. These methods have been used to investigate the macro- and microevolution of a broad range of organisms, including humans. Here, we provide a comprehensive outline of these methods, explaining their conceptual motivations and statistical interpretations. We highlight areas of recent and future development in evolutionary genomics methods and discuss ongoing challenges for researchers employing such tests. In particular, we emphasize the importance of functional follow-up studies to characterize putative selected alleles and the use of selection scans as hypothesis-generating tools for investigating evolutionary histories.