Fisher's theory of sexual selection, Wright's shifting-balance theory, and recent models based on them are reviewed as mechanisms of animal speciation. The joint evolution of mating preferences and secondary sexual characters can cause rapid nonadaptive phenotypic divergence and premating isolation between geographically separated populations, or along a cline. Extensive comparative data on Drosophila species support the suggestion of R. A. Fisher and T. Dobzhansky that the evolution of mating preferences can reinforce partial postmating isolation between sympatric populations. The interaction of natural selection and random genetic drift in local populations with a small effective size can produce a rapid transition between relatively stable phenotypes separated by an adaptive valley, or between chromosomal rearrangements with a heterozygote disadvantage. Large demographic fluctuations, such as frequent random local extinction and colonization, are required for the rapid spread of new adaptations (or karyotypes) when intermediate phenotypes (or rearrangement heterozygotes) are selected against.