The human Y chromosome is male-sex-determining and haploid, and so escapes recombination for most of its length. Haplotypes, which can be defined by the many binary markers and microsatellites that are available, pass down paternal lineages and change only by mutation.A small effective population size and the practice of patrilocality accentuate drift, which leads to the marked geographical differentiation of Y haplotypes. This makes the Y chromosome a powerful tool for investigating events in human genetic history.The study of mutation on the Y chromosome clarifies intra-allelic processes in general, and provides specific information about mutation rates that is useful in estimating the coalescent times of lineages. Intrachromosomal paralogous sequences are plentiful and cause pathogenic and non-pathogenic structural rearrangements.Selection might be important in shaping Y-chromosome diversity in populations, but it has been difficult to identify. Some studies show associations between deleterious phenotypes and particular haplotypes, but these associations are weak; some coalescence times are younger than expected, which indicates recent selection, but these estimates are uncertain, and population phenomena might be an alternative explanation.The phylogeny of binary Y haplogroups is well established, but the dates of branchpoints are uncertain. Many populations have been poorly sampled, and there is ascertainment bias in the set of available binary markers.The recent coalescence time, rooting of the Y phylogeny in Africa and evidence for an 'Out-of-Africa' range expansion, all show that modern Y-chromosome diversity arose recently in Africa and replaced Y chromosomes elsewhere. The pattern of Y-chromosome variation broadly fits a model of a southern migration that reached Australia, and a northern migration into Eurasia.Many features of the patterns of modern Y-chromosome diversity reflect later range expansions and contractions that were driven by changes in climate and lifestyle. Long-term population size, social structures and social selection have also been important.Future developments in the field are likely to include more markers, and a move towards the unbiased resequencing of samples.Other parts of the genome might show a 'haplotype-block' structure that is made up of regions of strong linkage disequilibrium. If this is so, then methods pioneered in the analysis of the Y chromosome could be widely applicable.