Hybridization has many and varied impacts on the process of speciation. Hybridization may slow or reverse differentiation by allowing gene flow and recombination. It may accelerate speciation via adaptive introgression or cause near-instantaneous speciation by allopolyploidization. It may have multiple effects at different stages and in different spatial contexts within a single speciation event. We offer a perspective on the context and evolutionary significance of hybridization during speciation, highlighting issues of current interest and debate. In secondary contact zones, it is uncertain if barriers to gene flow will be strengthened or broken down due to recombination and gene flow. Theory and empirical evidence suggest the latter is more likely, except within and around strongly selected genomic regions. Hybridization may contribute to speciation through the formation of new hybrid taxa, whereas introgression of a few loci may promote adaptive divergence and so facilitate speciation. Gene regulatory networks, epigenetic effects and the evolution of selfish genetic material in the genome suggest that the Dobzhansky-Muller model of hybrid incompatibilities requires a broader interpretation. Finally, although the incidence of reinforcement remains uncertain, this and other interactions in areas of sympatry may have knock-on effects on speciation both within and outside regions of hybridization.