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Understanding and forecasting species' geographic distributions in the face of global change is a central priority in biodiversity science. The existing view is that one must choose between correlative models for many species versus process-based models for few species. We suggest that opportunities exist to produce process-based range models for many species, by using hierarchical and inverse modeling to borrow strength across species, fill data gaps, fuse diverse data sets, and model across biological and spatial scales. We review the statistical ecology and population and range modeling literature, illustrating these modeling strategies in action. A variety of large, coordinated ecological datasets that can feed into these modeling solutions already exist, and we highlight organisms that seem ripe for the challenge.