AbstractUnderstanding the likely future impacts of biological invasions is crucial yet highly challenging given the multiple relevant environmental, socio‐economic and societal contexts and drivers. In the absence of quantitative models, methods based on expert knowledge are the best option for assessing future invasion trajectories. Here, we present an expert assessment of the drivers of potential alien species impacts under contrasting scenarios and socioecological contexts through the mid‐21st century. Based on responses from 36 experts in biological invasions, moderate (20%–30%) increases in invasions, compared to the current conditions, are expected to cause major impacts on biodiversity in most socioecological contexts. Three main drivers of biological invasions—transport, climate change and socio‐economic change—were predicted to significantly affect future impacts of alien species on biodiversity even under a best‐case scenario. Other drivers (e.g. human demography and migration in tropical and subtropical regions) were also of high importance in specific global contexts (e.g. for individual taxonomic groups or biomes). We show that some best‐case scenarios can substantially reduce potential future impacts of biological invasions. However, rapid and comprehensive actions are necessary to use this potential and achieve the goals of the Post‐2020 Framework of the Convention on Biological Diversity.