Genome duplication represents a dramatic, yet relatively common, genomic change, having occurred in the evolutionary history of angiosperms, vertebrates, and yeast, among many other groups. The result of such duplications ('polyploidy,' the existence of multiple sets of chromosomes within the genome) has long been recognized and was implicated as a rapid route to speciation nearly a century ago. We review recent studies that clarify how often polyploid populations establish, as well as studies that investigate the impact of polyploidization on the diversification of descendant species. Although the contribution of polyploidization to evolutionary processes is becoming increasingly clear, we conclude with a discussion of what remains unknown about the contribution of polyploidization to the formation of new species.