Religious diversity has had profound consequences in human history, but the dynamics of how it evolves remain unclear. One unresolved question is the extent to which religious denominations accumulate gradually or are generated in rapid bursts associated with specific historical events. Anecdotal evidence tends to favour the second view, but quantitative evidence on a global scale is lacking. Phylogenetic methods that treat religious denominations as evolving lineages can help to resolve this question. Here we apply computational phylogenetic methods to a purpose-built data set documenting 291 religious denominations and their genealogical relationships to derive dated phylogenies of three families of world religions – Indo-Iranian, Islamic, and Judeo-Christian. We model the birth of new denominations along the branches of these phylogenies, test for shifts in the birth rate, and draw tentative links between the shifts we find and religious history. We find evidence for birth rate shifts in the Islamic and Judeo-Christian families, corresponding to at least three separate events that have shaped global religious diversity.