Body size correlates with virtually every aspect of species biology, so understanding the tempo and mode of its evolution is of key importance in macroecology and macroevolution. Here we use body mass data from 3,473 of 4,510 extant mammalian species and an almost complete species-level phylogeny to determine the best model of log(body mass) evolution across all mammals, split taxonomically and spatially. An early-burst model fits better across all mammals than do models based on either Brownian motion or an Ornstein-Uhlenbeck process, suggesting that mammals experienced a burst of morphological evolution relatively early in their history that was followed by slower change. We also use spatial models to investigate rates of body mass evolution within ecoregions. These models show that around 50% of the variation in rate can be explained by just a few predictors. High estimated rates are associated with cold, low-lying, species-poor, high-energy, mainland ecoregions. We conclude that the evolution of mammalian body size has been influenced by a complex interplay among geography, climate, and history.