The uneven distribution of species richness is a fundamental and unexplained pattern of vertebrate biodiversity. Although species richness in groups like mammals, birds, or teleost fishes is often attributed to accelerated cladogenesis, we lack a quantitative conceptual framework for identifying and comparing the exceptional changes of tempo in vertebrate evolutionary history. We develop MEDUSA, a stepwise approach based upon the Akaike information criterion for detecting multiple shifts in birth and death rates on an incompletely resolved phylogeny. We apply MEDUSA incompletely to a diversity tree summarizing both evolutionary relationships and species richness of 44 major clades of jawed vertebrates. We identify 9 major changes in the tempo of gnathostome diversification; the most significant of these lies at the base of a clade that includes most of the coral-reef associated fishes as well as cichlids and perches. Rate increases also underlie several well recognized tetrapod radiations, including most modern birds, lizards and snakes, ostariophysan fishes, and most eutherian mammals. In addition, we find that large sections of the vertebrate tree exhibit nearly equal rates of origination and extinction, providing some of the first evidence from molecular data for the importance of faunal turnover in shaping biodiversity. Together, these results reveal living vertebrate biodiversity to be the product of volatile turnover punctuated by 6 accelerations responsible for >85% of all species as well as 3 slowdowns that have produced "living fossils." In addition, by revealing the timing of the exceptional pulses of vertebrate diversification as well as the clades that experience them, our diversity tree provides a framework for evaluating particular causal hypotheses of vertebrate radiations.