Darwin's Origin of Species is often criticized for having little to say about speciation. The complaint focuses in particular on Darwin's supposed failure to explain the evolution of the sterility and inviability of interspecific hybrids. But in his chapter on hybridism, Darwin, working without genetics, got as close to the modern understanding of the evolution of hybrid sterility and inviability as might reasonably be expected. In particular, after surveying what was then known about interspecific crosses and the resulting hybrids, he established two facts that, while now taken for granted, were at the time radical. First, the sterility barriers between species are neither specially endowed by a creator nor directly favored by natural selection but rather evolve as incidental by-products of interspecific divergence. Second, the sterility of species hybrids results when their development is "disturbed by two organizations having been compounded into one." Bateson, Dobzhansky, and Muller later put Mendelian detail to Darwin's inference that the species-specific factors controlling development (i.e., genes) are sometimes incompatible. In this article, I highlight the major developments in our understanding of these interspecific genetic incompatibilities--from Darwin to Muller to modern theory--and review comparative, genetic, and molecular rules that characterize the evolution of hybrid sterility and inviability.