Abstract The use of species distribution models (SDM) is of increasing popularity when studying biological invasions, e.g. to assess the impact of climate change on invasive species, to prioritize conservation measures, or to study invasive evolutionary biology. SDM correlate known occurrences of species with environmental variables and predict a species' potential distribution on other geographies over space and time. Today, SDM are widely used to produce invasion risk maps by delineating probable risk areas based on climatic suitability for a species. These maps can guide early detection and rapid response measures. While recent developments in modelling approaches and wider availability of environment datasets have helped to create better and more accurate SDM, in many cases the used models ignore the associated underlying ecological processes for e.g. dispersal and biotic interactions and thus provide only an incomplete picture of invasion risks. In this paper, we present a review of the most common applications of SDM in invasive species management and provide an overview of possible solutions to various challenges like uncertainty and transferability associated with them. Based on our review we conclude that ways towards more accurate model outputs include fitting models with existing ecological knowledge (hybrid models), address uncertainty and biotic interactions and link species dispersal traits with projections of species distributions. In the future, work is required on developing more hybrid approaches and models that addresses both local diffusion and long distance movement of alien species.