The cultivated Brassica species include numerous vegetable and oil crops of global importance. Three genomes (designated A, B and C) share mesohexapolyploid ancestry and occur both singly and in each pairwise combination to define the Brassica species. With organizational errors (such as misplaced genome segments) corrected, we showed that the fundamental structure of each of the genomes is the same, irrespective of the species in which it occurs. This enabled us to clarify genome evolutionary pathways, including updating the Ancestral Crucifer Karyotype (ACK) block organization and providing support for the Brassica mesohexaploidy having occurred via a two-step process. We then constructed genus-wide pan-genomes, drawing from genes present in any species in which the respective genome occurs, which enabled us to provide a global gene nomenclature system for the cultivated Brassica species and develop a methodology to cost-effectively elucidate the genomic impacts of alien introgressions. Our advances not only underpin knowledge-based approaches to the more efficient breeding of Brassica crops but also provide an exemplar for the study of other polyploids.