We face an unprecedented threat from global alteration of nature and biodiversity, but we still lack rigorous estimates of how fast, where, and at which scales biodiversity changes. Studies report fragmented and seemingly contradictory results, suffer from mismatches in biodiversity metrics, mismatches in temporal and spatial grains, and are constrained by huge data gaps. Moreover, local loss and gain of biodiversity is decoupled from changes in countries or continents, with opposing directions at different scales being plausible. A quantitative synthesis that connects all this, and bridges the gaps, is needed. The objective of BEAST is to map and interpolate temporal biodiversity change in Europe, the US, and the world, across continuous space, time, and their grains, from locations as small as 1 m, to countries and continents, over the last ca 40 years, for birds, plants, and butterflies. To do this we will combine data from local time series with high-quality gridded atlas data from countries and continents. We will use a new cross-scale model to interpolate biodiversity change jointly across space and time, and across the data gaps. We will test if temporal change of diversity, distributions, and turnover can be estimated from: (i) static patterns of diversity and distributions, (ii) from data lacking temporal replication, (iii) from space-for-time substitution of spatial vs temporal species turnover, (iii) from spaceborne remotely sensed spectral diversity and turnover. These methods will enable integration of heterogeneous and messy biodiversity data, and they will improve estimates of change in data-poor regions of the global South. BEAST will deliver the first integrative statistical model revealing, for the first time, how multiple facets of biodiversity change across scales. It will show which regions, habitats, and biomes undergo the most pronounced change, which is critical for informed large-scale conservation policy.