The study of speciation has become one of the most active areas of evolutio
nary biology, and substantial progress has been made in documenting end und
erstanding 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 genera
lizations about data. Nevertheless, mathematical theory can provide a usefu
l classification of verbal theories; can help determine the biological plau
sibility of verbal theories; can determine whether alternative mechanisms o
f speciation are consistent with empirical patterns; and can occasionally p
rovide predictions that go beyond empirical generalizations. We discuss rec
ent examples of progress in each of these areas.