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 3473 of 4510 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 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 followed by slower change subsequently. 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.