Extreme climatic events (ECEs) – such as unusual heat waves, hurricanes, floods, and droughts – can dramatically affect ecological and evolutionary processes, and these events are projected to become more frequent and more intense with ongoing climate change. However, the implications of ECEs for biological invasions remain poorly understood. Using concepts and empirical evidence from invasion ecology, we identify mechanisms by which ECEs may influence the invasion process, from initial introduction through establishment and spread. We summarize how ECEs can enhance invasions by promoting the transport of propagules into new regions, by decreasing the resistance of native communities to establishment, and also sometimes by putting existing non-native species at a competitive disadvantage. Finally, we outline priority research areas and management approaches for anticipating future risks of unwanted invasions following ECEs. Given predicted increases in both ECE occurrence and rates of species introductions around the globe during the coming decades, there is an urgent need to understand how these two processes interact to affect ecosystem composition and functioning.