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Prediction of species’ distributions is central to diverse applications in ecology, evolution and conservation science. There is increasing electronic access to vast sets of occurrence records in museums and herbaria, yet little effective guidance on how best to use this information in the context of numerous approaches for modelling distributions. To meet this need, we compared 16 modelling methods over 226 species from 6 regions of the world, creating the most comprehensive set of model comparisons to date. We used presence‐only data to fit models, and independent presence‐absence data to evaluate the predictions. Along with well‐established modelling methods such as generalised additive models and GARP and BIOCLIM, we explored methods that either have been developed recently or have rarely been applied to modelling species’ distributions. These include machine‐learning methods and …