Ongoing and predicted global change makes understanding and predicting species' range shifts an urgent scientific priority. Here, we provide a synthetic perspective on the so far poorly understood effects of interspecific interactions on range expansion rates. We present theoretical foundations for how interspecific interactions may modulate range expansion rates, consider examples from empirical studies of biological invasions and natural range expansions as well as process-based simulations, and discuss how interspecific interactions can be more broadly represented in process-based, spatiotemporally explicit range forecasts. Theory tells us that interspecific interactions affect expansion rates via alteration of local population growth ra...