The origin and expansion of biological diversity is regulated by both developmental trajectories and limits on available ecological niches. As lineages diversify, an early and often rapid phase of species and trait proliferation gives way to evolutionary slow-downs as new species pack into ever more densely occupied regions of ecological niche space. Small clades such as Darwin's finches demonstrate that natural selection is the driving force of adaptive radiations, but how microevolutionary processes scale up to shape the expansion of phenotypic diversity over much longer evolutionary timescales is unclear. Here we address this problem on a global scale by analysing a crowdsourced dataset of three-dimensional scanned bill morphology from more than 2,000 species. We find that bill diversity expanded early in extant avian evolutionary history, before transitioning to a phase dominated by packing of morphological space. However, this early phenotypic diversification is decoupled from temporal variation in evolutionary rate: rates of bill evolution vary among lineages but are comparatively stable through time. We find that rare, but major, discontinuities in phenotype emerge from rapid increases in rate along single branches, sometimes leading to depauperate clades with unusual bill morphologies. Despite these jumps between groups, the major axes of within-group bill-shape evolution are remarkably consistent across birds. We reveal that macroevolutionary processes underlying global-scale adaptive radiations support Darwinian and Simpsonian ideas of microevolution within adaptive zones and accelerated evolution between distinct adaptive peaks.