Polyploidy, which arises through complex genetic and ecological processes, is an important mode of plant speciation. This review provides an overview of recent advances in understanding why plant polyploid species are so ubiquitous and diverse. We consider how the modern framework for understanding genetic mechanisms of speciation could be used to study allopolyploid speciation that occurs through hybrid genome doubling, that is, whole genome doubling of interspecific F1 hybrids by the union of male and female unreduced gametes. We outline genetic and ecological mechanisms that may have positive or negative impacts on the process of allopolyploid speciation through hybrid genome doubling. We also discuss the current status of studies on the underlying genetic mechanisms focusing on the wheat (Triticum and Aegilops) hybrid-specific reproductive phenomena that are well known but deserve renewed attention from an evolutionary viewpoint. © 2014 Elsevier Inc.