During the past decade there has been a tremendous resurgence of interest in polyploidy that has in large part been stimulated by the development of increasingly powerful genetic and genomic tools. The result has been numerous new insights into the genomic and genetic consequences of polyploidy. The plethora of new discoveries has dramatically reshaped traditional views and concomitantly revealed that polyploidy is a highly dynamic and ubiquitous process. These recent advances in our understanding of polyploidy have stimulated numerous reviews, most focused on the various genetic, epigenetic, and genomic consequences of polyploid evolution. Whereas genetic and genomic attributes of polyploidization have received considerable attention, other crucial areas of polyploid evolution have received much less (e.g., ecology, pollination biology, physiology). The focus of this paper is not to review again recent discoveries, but to emphasize what we do not yet know about polyploidy, which despite all that has been learned about genome doubling is still an enormous amount. Our list is not meant to be comprehensive, but includes a range of topics that we have placed in several general categories, including mode of formation, ecological and physiological consequences, and genomic rules. Questions include: What is (are) the most frequent mechanism(s) of polyploidization? What factors promote/facilitate polyploidization? What factors favor autopolyploid vs. allopolyploid formation? Do multiple origins result in lineages with differing evolutionary trajectories and/or cryptic species? Our major goals are to stimulate discussion and promote further research.