Genomic evidence of ancestral whole genome duplication (WGD) and polyploidy is widespread among eukaryotic species, and especially among plants. WGD is thought to provide the raw material for adaptation in the form of duplicated genes, and polyploids are thought to benefit from both physiological and genetic buffering. Comparatively little attention has focused on the genomic challenge of polyploidy, however, although much evidence exists that polyploidy severely perturbs important cellular functions. Here, I review recent progress in the study of the re-establishment of stable meiosis in recently evolved polyploids, focusing on four plant species. This work has yielded an insight into the mechanisms underlying stabilization of genome transmission in polyploids, and is revealing remarkable parallels among diverse taxa. Importantly, these studies also provide a road map for investigating how polyploids respond to the challenge of WGD.