The study of speciation has become one of the most active areas of evolutionary biology, and substantial progress has been made in documenting and understanding phenomena ranging from sympatric speciation and reinforcement to the evolutionary genetics of postzygotic isolation. This progress has been driven largely by empirical results, and most useful theoretical work has concentrated on making sense of empirical patterns. Given the complexity of speciation, mathematical theory is subordinate to verbal theory and generalizations about data. Nevertheless, mathematical theory can provide a useful classification of verbal theories; can help determine the biological plausibility of verbal theories; can determine whether alternative mechanisms of speciation are consistent with empirical patterns; and can occasionally provide predictions that go beyond empirical generalizations. We discuss recent examples of progress in each of these areas.