Genomic technologies for livestock and companion animal species have revolutionized the study of animal domestication, allowing an increasingly detailed description of the genetic changes accompanying domestication and breed development. This review describes important recent results derived from the application of population and quantitative genetic approaches to the study of genetic changes in the major domesticated species. These include findings of regions of the genome that show between-breed differentiation, evidence of selective sweeps within individual genomes and signatures of demographic events. Particular attention is focused on the study of the genetics of behavioural traits and the implications for domestication. Despite the operation of severe bottlenecks, high levels of inbreeding and intensive selection during the history of domestication, most domestic animal species are genetically diverse. Possible explanations for this phenomenon are discussed. The major insights from the surveyed studies are highlighted and directions for future study are suggested.