Polyploidy is a major force in plant evolution and speciation. In newly formed allopolyploids, pairing between related chromosomes from different subgenomes (homoeologous chromosomes) during meiosis is common. The initial stages of allopolyploid formation are characterized by a spectrum of saltational genomic and regulatory alterations that are responsible for evolutionary novelty. Here we highlight the possible effects and roles of recombination between homoeologous chromosomes during the early stages of allopolyploid stabilization. Homoeologous exchanges (HEs) have been reported in young allopolyploids from across the angiosperms. Although all lineages undergo karyotype change via chromosome rearrangements over time, the early generations after allopolyploid formation are predicted to show an accelerated rate of genomic change. HEs can also cause changes in allele dosage, genome-wide methylation patterns, and downstream phenotypes, and can hence be responsible for speciation and genome stabilization events. Additionally, we propose that fixation of duplication – deletion events resulting from HEs could lead to the production of genomes which appear to be a mix of autopolyploid and allopolyploid segments, sometimes termed “segmental allopolyploids.” We discuss the implications of these findings for our understanding of the relationship between genome instability in novel polyploids and genome evolution.