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Knowing where species occur is fundamental to many ecological and environmental applications. Species distribution models (SDMs) are typically based on correlations between species occurrence data and environmental predictors, with ecological processes captured only implicitly. However, there is a growing interest in approaches that explicitly model processes such as physiology, dispersal, demography and biotic interactions. These models are believed to offer more robust predictions, particularly when extrapolating to novel conditions. Many process-explicit approaches are now available, but it is not clear how we can best draw on this expanded modelling toolbox to address ecological problems and inform management decisions. Here, we review a range of process-explicit models to determine their strengths and limitations, as well as their current use. Focusing on four common applications of SDMs - regulatory planning, extinction risk, climate refugia and invasive species - we then explore which models best meet management needs. We identify barriers to more widespread and effective use of process-explicit models and outline how these might be overcome. As well as technical and data challenges, there is a pressing need for more thorough evaluation of model predictions to guide investment in method development and ensure the promise of these new approaches is fully realised.