The selection of desirable traits in crops during domestication has been well studied. Many crops share a suite of modified phenotypic characteristics collectively known as the domestication syndrome. In this sense, crops have convergently evolved. Previous work has demonstrated that, at least in some instances, convergence for domestication traits has been achieved through parallel molecular means. However, both demography and selection during domestication may have placed limits on evolutionary potential and reduced opportunities for convergent adaptation during post-domestication migration to new environments. Here we review current knowledge regarding trait convergence in the cereal grasses and consider whether the complexity and dynamism of cereal genomes (e.g., transposable elements, polyploidy, genome size) helped these species overcome potential limitations owing to domestication and achieve broad subsequent adaptation, in many cases through parallel means. This article is part of the theme issue 'Convergent evolution in the genomics era: new insights and directions'.