Polyploidy has played a major role in the evolution of many eukaryotes. Recent studies have dramatically reshaped views of polyploid evolution, demonstrating that most polyploid species examined, both plant and animal, have formed recurrently from different populations of their progenitors. Populations of independent origin can subsequently come into contact and hybridize, generating new genotypes. Because of the frequency of polyploidy in plants, many recognized species are probably polyphyletic. Extensive and rapid genome restructuring can occur after polyploidization. Such changes can be mediated by transposons. Polyploidization could represent a period of transilience, during which genomic changes occur, potentially producing new gene complexes and facilitating rapid evolution.