Polyploidy, or whole-genome duplication (WGD), is an important genomic feature for all eukaryotes, especially many plants and some animals. The common occurrence of polyploidy suggests an evolutionary advantage of having multiple sets of genetic material for adaptive evolution. However, increased gene and genome dosages in autopolyploids (duplications of a single genome) and allopolyploids (combinations of two or more divergent genomes) often cause genome instabilities, chromosome imbalances, regulatory incompatibilities, and reproductive failures. Therefore, new allopolyploids must establish a compatible relationship between alien cytoplasm and nuclei and between two divergent genomes, leading to rapid changes in genome structure, gene expression, and developmental traits such as fertility, inbreeding, apomixis, flowering time, and hybrid vigor. Although the underlying mechanisms for these changes are poorly understood, some themes are emerging. There is compelling evidence that changes in DNA sequence, cis- and trans-acting effects, chromatin modifications, RNA-mediated pathways, and regulatory networks modulate differential expression of homoeologous genes and phenotypic variation that may facilitate adaptive evolution in polyploid plants and domestication in crops.