Background: Barley is one of the founder crops of Neolithic agriculture and is among the most-grown cereals today. The only trait that universally differentiates the cultivated and wild subspecies is 'non-brittleness' of the rachis (the stem of the inflorescence), which facilitates harvesting of the crop. Other phenotypic differences appear to result from facultative or regional selective pressures. The population structure resulting from these regional events has been interpreted as evidence for multiple domestications or a mosaic ancestry involving genetic interaction between multiple wild or proto-domesticated lineages. However, each of the three mutations that confer nonbrittleness originated in the western Fertile Crescent, arguing against multiregional origins for the crop. Results: We examined exome data for 310 wild, cultivated and hybrid/feral barley accessions and showed that cultivated barley is structured into six genetically-defined groups that display admixture, resulting at least in part from two or more significant passages of gene flow with distinct wild populations. The six groups are descended from a single founding population that emerged in the western Fertile Crescent. Only a few loci were universally targeted by selection, the identity of these suggesting that changes in seedling emergence and pathogen resistance could represent crucial domestication switches. Subsequent selection operated on a regional basis and strongly contributed to differentiation of the genetic groups. Conclusions: Identification of genetically-defined groups provides clarity to our understanding of the population history of cultivated barley. Inference of population splits and mixtures together with analysis of selection sweeps indicate descent from a single founding population, which emerged in the western Fertile Crescent. This founding population underwent relatively little genetic selection, those changes that did occur affecting traits involved in seedling emergence and pathogen resistance, indicating that these phenotypes should be considered as 'domestication traits'. During its expansion out of the western Fertile Crescent, the crop underwent regional episodes of gene flow and selection, giving rise to a modern genetic signature that has been interpreted as evidence for multiple domestications, but which we show can be rationalized with a single origin.