Historical biogeography has recently experienced a significant advancement in three integrated areas. The first is the adoption of an ontology of complexity, replacing the traditional ontology of simplicity, or a priori parsimony; simple and elegant models of the biosphere are not sufficient for explaining the geographical context of the origin of species and their post-speciation movements, producing evolutionary radiations and complex multi-species biotas. The second is the development of a powerful method for producing area cladograms from complex data, especially cases of reticulated area relationships, without loss of information. That method, called Phylogenetic Analysis for Comparing trees (PACT), is described herein. The third element is the replacement of the model of maximum vicariance with the model called the Taxon Pulse hypothesis. PACT analysis of Hominoidea, Hyaenidae, and Proboscidea beginning in the Miocene, reveals that all three groups share a general episode of species formation in Africa in the early Miocene, followed by “out of Africa” expansion into Europe, Asia and North America, a second general episode of species formation in Asia in the mid-Miocene, followed by “out of Asia” expansion into Africa, Europe and North America. Finally, there were two additional “out of Africa” events during the late Miocene and into the Pliocene, the last one setting the stage for the emergence and spread of Homo. In addition to these shared episodes of vicariance and dispersal, each group exhibits clade-specific within-area and peripheral isolates speciation events. The complex history of dispersal and speciation over large areas exhibited by hominoids is part of a more general history of biotic diversification by taxon pulses.