Polyploidization and recombination are two important processes driving evolution through the building and reshaping of genomes. Allopolyploids arise from hybridization and chromosome doubling among distinct, yet related species. Polyploids may display novel variation relative to their progenitors, and the sources of this variation lie not only in the acquisition of extra gene dosages, but also in the genomic changes that occur after divergent genomes unite. Genomic changes (deletions, duplications, and translocations) have been detected in both recently formed natural polyploids and resynthesized polyploids. In resynthesized Brassica napus allopolyploids, there is evidence that many genetic changes are the consequence of homoeologous recombination. Homoeologous recombination can generate novel gene combinations and phenotypes, but may also destabilize the karyotype and lead to aberrant meiotic behavior and reduced fertility. Thus, natural selection plays a role in the establishment and maintenance of fertile natural allopolyploids that have stabilized chromosome inheritance and a few advantageous chromosomal rearrangements. We discuss the evidence for genome rearrangements that result from homoeologous recombination in resynthesized B. napus and how these observations may inform phenomena such as chromosome replacement, aneuploidy, non-reciprocal translocations and gene conversion seen in other polyploids.