Perhaps all flowering plants have experienced one or more episodes of polyploidization at some time in their evolutionary history. Recent evidence indicates that this genome doubling may be accompanied by a variety of non- Mendelian phenomena, some of which operate during hybridization and polyploid formation while others manifest more gradually on an evolutionary timescale. Here we review these phenomena, drawing attention to recent paradigm shifts necessitated by new insights from model plant systems. Allopolyploid formation in some plant groups is associated with an unexplained and in some cases directed process of genomic alteration leading to non-additivity with respect to parental genomes. Novel intergenomic interactions become possible as a consequence of the merger of two previously isolated diploid genomes, variously leading to intergenomic colonization and / or homogenization of formerly diverged sequences. Several epigenetic processes may accompany nascent allopolyploidy, such as nucleolar dominance, gene silencing and mobile element activation, the latter also resulting in genetic change. These myriad phenomena do not characterize all polyploid systems, and some nascent allopolyploids appear to be genomically quiescent. Although a direct connection to adaptation remains to be established, the diversity of genetic responses to allopolyploid formation and their apparent high frequency suggest that non-Mendelian phenomena contribute directly to polyploid stabilization and diversification.