Polyploidy, or the presence of two or more diploid parental genome sets within an organism, is found to an amazing degree in higher plants. In addition, many plant species traditionally considered to be diploid have recently been demonstrated to have undergone rounds of genome duplication in the past and are now referred to as paleopolyploids. Polyploidy and interspecific hybridisation (with which it is often associated) have long been thought to be important mechanisms of rapid species formation. The widespread occurrence of polyploids, which are frequently found in habitats different from that of their diploid progenitors, would seem to indicate that polyploidy is associated with evolutionary success in terms of the ability to colonise new environmental niches. A flurry of recent genomic studies has provided fresh insights into the potential basis of the phenotypic novelty of polyploid species. Here we review current knowledge of genetic, epigenetic, and transcriptional changes associated with polyploidy in plants and assess how these changes might contribute to the evolutionary success of polyploid plants. We conclude by stressing the need for field-based experiments to determine whether genetic changes associated with polyploidy are indeed adaptive.