Domestication of plants and animals is the major factor underlying human civilization and is a gigantic evolutionary experiment of adaptation and speciation, generating incipient species. Wheat is one of the most important grain crops in the world, and consists mainly of two types: the hexaploid bread wheat (Triticum aestivum) accounting for about 95% of world wheat production, and the tetraploid durum wheat (T. durum) accounting for the other 5%. In this review, we summarize and discuss research on wheat domestication, mainly focusing on recent findings in genetics and genomics studies. T. aestivum originated from a cross between domesticated emmer wheat T. dicoccum and the goat grass Aegilops tauschii, most probably in the south and west of the Caspian Sea about 9,000 years ago. Wild emmer wheat has the same genome formula as durum wheat and has contributed two genomes to bread wheat, and is central to wheat domestication. Domestication has genetically not only transformed the brittle rachis, tenacious glume and non-free threshability, but also modified yield and yield components in wheat. Wheat domestication involves a limited number of chromosome regions, or domestication syndrome factors, though many relevant quantitative trait loci have been detected. On completion of the genome sequencing of diploid wild wheat (T. urartu or Ae. tauschii), domestication syndrome factors and other relevant genes could be isolated, and effects of wheat domestication could be determined. The achievements of domestication genetics and robust research programs in Triticeae genomics are of greatly help in conservation and exploitation of wheat germplasm and genetic improvement of wheat cultivars.