Climate change and biological invasions are threatening biodiversity and ecosystem services worldwide. It has now been widely acknowledged that climate change will affect biological invasions. A large number of studies have investigated predicted shifts and other changes in the geographic ranges of invasive alien species related to climate change using modeling approaches. Yet these studies have provided contradictory evidence, and no consensus has been reached. We conducted a systematic review of 423 modeling case studies included in 71 publications that have examined the predicted effects of climate change on those species. We differentiate the approaches used in these studies and synthesize their main results. Our results reaffirm the major role of climate change as a driver of invasive alien species distribution in the future. We found biases in the literature both regarding the taxa, toward plants and invertebrates, and the areas of the planet investigated. Despite these biases, we found for the plants and vertebrates studied that climate change will more frequently contribute to a decrease in species range size than an increase in the overall area occupied. This is largely due to oceans preventing terrestrial invaders from spreading poleward. In contrast, we found that the ranges of invertebrates and pathogens studied are more likely to increase following climate change. An important caveat to these findings is that researchers have rarely considered the effects of climate change on transport, introduction success, or the resulting impacts. We recommend closing these research gaps, and propose additional avenues for future investigations, as well as opportunities and challenges for managing invasions under climate change.