Technical Abstract: Extreme climatic events, such as intense heat waves, hurricanes, floods and droughts, can dramatically affect ecological and evolutionary processes, and more extreme events are projected with ongoing climate change. However, the implications of these events for biological invasions, which themselves can disrupt ecosystems, remain poorly understood. Here, we review evidence that extreme climatic events influence the invasion process, from initial introduction through establishment and spread, and identify mechanisms by which this may occur. We show how extreme events can reduce resistance to invasions, but also sometimes disadvantage established invaders. We use this review to outline priority research areas and management approaches for anticipating future risks of unwanted invasions following extreme events. Given predicted increases in both extreme events 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.