Human activities are fundamentally altering biodiversity. Projections of declines at the global scale are contrasted by highly variable trends at local scales, suggesting that biodiversity change may be spatially structured. Here, we examined spatial variation in species richness and composition change using more than 50,000 biodiversity time series from 239 studies and found clear geographic variation in biodiversity change. Rapid compositional change is prevalent, with marine biomes exceeding and terrestrial biomes trailing the overall trend. Assemblage richness is not changing on average, although locations exhibiting increasing and decreasing trends of up to about 20% per year were found in some marine studies. At local scales, widespread compositional reorganization is most often decoupled from richness change, and biodiversity change is strongest and most variable in the oceans.