Polyploidy is a prominent process in plants and has been significant in the evolutionary history of vertebrates and other eukaryotes. In plants, interdisciplinary approaches combining phylogenetic and molecular genetic perspectives have enhanced our awareness of the myriad genetic interactions made possible by polyploidy. Here, processes and mechanisms of gene and genome evolution in polyploids are reviewed. Genes duplicated by polyploidy may retain their original or similar function, undergo diversification in protein function or regulation, or one copy may become silenced through mutational or epigenetic means. Duplicated genes also may interact through inter-locus recombination, gene conversion, or concerted evolution. Recent experiments have illuminated important processes in polyploids that operate above the organizational level of duplicated genes. These include inter-genomic chromosomal exchanges, saltational, non-Mendelian genomic evolution in nascent polyploids, inter-genomic invasion, and cytonuclear stabilization. Notwithstanding many recent insights, much remains to be learned about many aspects of polyploid evolution, including: the role of transposable elements in structural and regulatory gene evolution; processes and significance of epigenetic silencing; underlying controls of chromosome pairing; mechanisms and functional significance of rapid genome changes; cytonuclear accommodation; and coordination of regulatory factors contributed by two, sometimes divergent progenitor genomes. Continued application of molecular genetic approaches to questions of polyploid genome evolution holds promise for producing lasting insight into processes by which novel genotypes are generated and ultimately into how polyploidy facilitates evolution and adaptation.