Phylogenies reconstructed from gene sequences can be used to investigate the tempo and mode of species diversification. Here we develop and use new statistical methods to infer past patterns of speciation and extinction from molecular phylogenies. Specifically, we test the null hypothesis that per–lineage speciation and extinction rates have remained constant through time. Rejection of this hypothesis may provide evidence for evolutionary events such as adaptive radiations or key adaptations. In contrast to previous approaches, our methods are robust to incomplete taxon sampling and are conservative with respect to extinction. Using simulation we investigate, first, the adverse effects of failing to take incomplete sampling into account and, second, the power and reliability of our tests. When applied to published phylogenies our tests suggest that, in some cases, speciation rates have decreased through time.