We need accurate predictions about how climate change will alter species distributions and abundances around the world. Most predictions assume simplistic dispersal scenarios and ignore biotic interactions. We argue for incorporating the complexities of dispersal and species interactions. Range expansions depend not just on mean dispersal, but also on the shape of the dispersal kernel and the population's growth rate. We show how models using species-specific dispersal can produce more accurate predictions than models applying all-or-nothing dispersal scenarios. Models that additionally include species interactions can generate distinct outcomes. For example, species interactions can slow climate tracking and produce more extinctions than models assuming no interactions. We conclude that (1) just knowing mean dispersal is insufficient to predict biotic responses to climate change, and (2) considering interspecific dispersal variation and species interactions jointly will be necessary to anticipate future changes to biological diversity. We advocate for collecting key information on interspecific dispersal differences and strong biotic interactions so that we can build the more robust predictive models that will be necessary to inform conservation efforts as climates continue to change.