Abstract Background and Aims The development and morphology of crop plants have been profoundly altered by evolution under cultivation, initially through unconscious selection, without deliberate foresight, and later by directed breeding. Wild wheats remain an important potential source of variation for modern breeders; however, the sequence and timing of morphological changes during domestication are not fully resolved. Methods We grew and measured 142 wheat accessions representing different stages in wheat evolution, including three independent domestication events, and compared their morphological traits to define the morphospace of each group. Key Results The results show that wild and domesticated wheats have overlapping morphospaces, but each also occupies a distinct area of morphospace from one another. Polyploid formation in wheat increased leaf biomass and seed weight but had its largest effects on tiller loss. Domestication continued to increase the sizes of wheat leaves and seeds and made wheat grow taller, with more erect architecture. Associated changes to the biomass of domesticated wheats generated more grains and achieved higher yields. Landrace improvement subsequently decreased the numbers of tillers and spikes, to focus resource allocation to the main stem, accompanied by a thicker main stem and larger flag leaves. During the Green Revolution, wheat height was reduced to increase the harvest index and therefore yield. Modern wheats also have more erect leaves and larger flower biomass proportions than landraces. Conclusions Quantitative trait history in wheat differs by trait. Some trait values show progressive changes in the same direction (e.g. leaf size, grain weight), whereas others change in a punctuated way at particular stages (e.g. canopy architecture), and other trait values switch directions during wheat evolution (e.g. plant height, flower biomass proportion). Agronomically valued domestication traits arose during different stages of wheat history, such that modern wheats are the product of >10 000 years of morphological evolution.