Abstract Risk maps are a useful tool to prioritise sites for management and allocate resources where they are most needed as they can show us where impacts of biological invasions are most likely to happen or expected to be largest. Given the pace of global changes, we need to understand not only the risks under current conditions, but future risks taking these changes into account. In this study, we use Australian acacias alien to South Africa as a case study to model their potential distribution under future climate change to map their potential impacts at the middle and end of the century and the uncertainty related to three socio-economic pathways and five climatic models. The resulting risk maps across South Africa are a pioneering attempt to combine impacts of alien species with potential future distributions. We found that although climatic suitability and therefore the risk is predicted to decrease under climate change in 51,4% of the country’s area, the opposite is predicted for 26% of the area and the highly vulnerable fynbos biome remains an area with high projected impacts. Such risk maps can help us prioritise management actions and aid the development of suitable plans to protect biodiversity under current and future climate conditions. However, they have to be interpreted with caution and we highlight some shortcomings around species distribution models in general, vulnerability of ecosystems to the potential impacts, data gaps on impacts, as well as currently benign or unknown invaders, which are not included in the projections.