Degree of genetic divergence is frequently used to infer that two populations belong to separate species, or that several populations belong to a single species. I explore the logical framework of this approach, including the following assumptions: (i) speciation takes place over very long periods of time; (ii) reproductive isolation is based on the slow accumulation many genetic differences throughout the genome; (iii) genetic divergence automatically leads to reproductive isolation between species; and (iv) pre-mating and post-mating reproductive isolation have a similar genetic basis. I argue that so many exceptions to these assumptions have been demonstrated that they cannot be used with any reliability to distinguish different species. In addition, genetic distance as a species criterion is mostly used within the framework of Mayr's Biological Species Concept and is not free of assumptions about the nature of species or of speciation. The use of genetic distance to infer separate species (or the lack of these) is not parsimonious, its theoretical foundations are not well understood, and it cannot be applied over a wide range of plants and animals. I explore alternative approaches towards solving the species problems normally solved using genetic distance. © 2002 The Linnean Society of London, Biological Journal of the Linnean Society, 2002, 75, 509–516.