The last decade highlighted polyploidy as a rampant evolutionary process that triggers drastic genome reorganization, but much remains to be understood about their causes and consequences in both autopolyploids and allopolyploids. Here, we provide an overview of the current knowledge on the pathways leading to different types of polyploids and patterns of polyploidy-induced genome restructuring and functional changes in plants. Available evidence leads to a tentative ‘diverge, merge and diverge' model supporting polyploid speciation and stressing patterns of divergence between diploid progenitors as a suitable predictor of polyploid genome reorganization. The merging of genomes at the origin of a polyploid lineage may indeed reveal different kinds of incompatibilities (chromosomal, genic and transposable elements) that have accumulated in diverging progenitors and reduce the fitness of nascent polyploids. Accordingly, successful polyploids have to overcome these incompatibilities through non-Mendelian mechanisms, fostering polyploid genome reorganization in association with the establishment of new lineages. See also sister article focusing on animals by Collares-Pereira et al., in this themed issue.