Newly formed polyploids often show extensive meiotic defects, resulting in aneuploid gametes, and thus reduced fertility. However, while many neopolyploids are meiotically unstable, polyploid lineages that survive in nature are generally stable and fertile; thus, those lineages that survive are those that are able to overcome these challenges. Several genes that promote polyploid stabilization are now known in plants, allowing speculation on the evolutionary origin of these meiotic adjustments. Here, I discuss results that show that meiotic stability can be achieved through the differentiation of certain alleles of certain genes between ploidies. These alleles, at least sometimes, seem to arise by novel mutation, while standing variation in either ancestral diploids or related polyploids, from which alleles can introgress, may also contribute. Growing evidence also suggests that the coevolution of multiple interacting genes has contributed to polyploid stabilization, and in allopolyploids, the return of duplicated genes to single copies (genome fractionation) may also play a role in meiotic stabilization. There is also some evidence that epigenetic regulation may be important, which can help explain why some polyploid lineages can partly stabilize quite rapidly.