Phylogenetic relationships, divergence times, and patterns of biogeographic descent among primate species are both complex and contentious. Here, we generate a robust molecular phylogeny for 70 primate genera and 367 primate species based on a concatenation of 69 nuclear gene segments and ten mitochondrial gene sequences, most of which were extracted from GenBank. Relaxed clock analyses of divergence times with 14 fossil-calibrated nodes suggest that living Primates last shared a common ancestor 71-63 Ma, and that divergences within both Strepsirrhini and Haplorhini are entirely post-Cretaceous. These results are consistent with the hypothesis that the Cretaceous-Paleogene mass extinction of non-avian dinosaurs played an important role in the diversification of placental mammals. Previous queries into primate historical biogeography have suggested Africa, Asia, Europe, or North America as the ancestral area of crown primates, but were based on methods that were coopted from phylogeny reconstruction. By contrast, we analyzed our molecular phylogeny with two methods that were developed explicitly for ancestral area reconstruction, and find support for the hypothesis that the most recent common ancestor of living Primates resided in Asia. Analyses of primate macroevolutionary dynamics provide support for a diversification rate increase in the late Miocene, possibly in response to elevated global mean temperatures, and are consistent with the fossil record. By contrast, diversification analyses failed to detect evidence for rate-shift changes near the Eocene-Oligocene boundary even though the fossil record provides clear evidence for a major turnover event ("Grande Coupure") at this time. Our results highlight the power and limitations of inferring diversification dynamics from molecular phylogenies, as well as the sensitivity of diversification analyses to different species concepts.