The crop species within the genus Brassica have highly replicated genomes. Three base ‘diploid’ species, Brassica oleracea, B. nigra and B. rapa, are likely ancient polyploids, and three derived allopolyploid species, B. carinata, B. juncea and B. napus, are created from the interspecific hybridization of these base genomes. The base Brassica genome is thought to have hexaploid ancestry, and both recent and ancient polyploidization events have been proposed to generate a large number of genome rearrangements and novel genetic variation for important traits. Here, we revisit and refine these hypotheses. We have examined the B. oleracea linkage map using the Arabidopsis thaliana genome sequence as a template and suggest that there is strong evidence for genome replication and rearrangement within the base Brassicas, but less evidence for genome triplication. We show that novel phenotypic variation within the base Brassicas can be achieved by replication of a single gene, BrFLC, that acts additively to influence flowering time. Within the derived allopolyploids, intergenomic heterozygosity is associated with higher seed yields. Some studies have reported that de novo genomic variation occurs within derived polyploid genomes, whereas other studies have not detected these changes. We discuss reasons for these different findings. Large translocations and tetrasomic inheritance can explain some but not all genomic changes within the polyploids. Transpositions and other small-scale sequence changes probably also have contributed to genomic novelty. Our results have shown that the Brassica genomes are remarkably plastic, and that polyploidy generates novel genetic variation through gene duplication, intergenomic heterozygosity and perhaps epigenetic change. © 2004 The Linnean Society of London, Biological Journal of the Linnean Society, 2004, 82, 665–674.