This open access book covers a century of research on wheat genetics and evolution, starting with the discovery in 1918 of the accurate number of chromosomes in wheat. We re-evaluate classical studies that are pillars of the current knowledge considering recent genomic data in the wheat group comprising 31 species from the genera Amblyopyrum, Aegilops, Triticum, and other more distant relatives. For these species, we describe morphology, ecogeographical distribution, phylogeny as well as cytogenetic and genomic features. For crops, we also address evolution under human selection, namely pre-domestication cultivation and domestication. We re-examine the genetic and archeological evidence of where, when, and how domestication occurred. We discuss unique aspects of genome evolution and maintenance under polyploidization, in natural and synthetic allopolyploids of the wheat group. Finally, we propose some thoughts on the future prospects of wheat improvement. As such, it can be of great interest to wheat researchers and breeders as well as to plant scientists and students interested in plant genetics, evolution, domestication, and polyploidy.