AbstractHalf a century ago, a seminal article on the hitchhiking effect by Smith and Haigh inaugurated the concept of the selection signature. Selective sweeps are characterised by the rapid spread of an advantageous genetic variant through a population and hence play an important role in shaping evolution and research on genetic diversity. The process by which a beneficial allele arises and becomes fixed in a population, leading to a increase in the frequency of other linked alleles, is known as genetic hitchhiking or genetic draft. Kimura's neutral theory and hitchhiking theory are complementary, with Kimura's neutral evolution as the ‘null model’ and positive selection as the ‘signal’. Both are widely accepted in evolution, especially with genomics enabling precise measurements. Significant advances in genomic technologies, such as next‐generation sequencing, high‐density SNP arrays and powerful bioinformatics tools, have made it possible to systematically investigate selection signatures in a variety of species. Although the history of selection signatures is relatively recent, progress has been made in the last two decades, owing to the increasing availability of large‐scale genomic data and the development of computational methods. In this review, we embark on a journey through the history of research on selective sweeps, ranging from early theoretical work to recent empirical studies that utilise genomic data.