In media reports and public debates, climate change has often been depicted as a major reason for expecting massively increasing migration flows. In the future, more and more people would be on the run from extreme weather events, looking for new places to live as a growing share of their current habitats turn uninhabitable. As such, climate-driven migration would add to already ongoing flows due to global socioeconomic inequality. However, according to recent scholarly literature, such claims are based on speculation rather than based on solid scientific reasoning and evidence. This paper aims to review both the theoretical reasons and empirical evidence gathered so far about climate-induced migration. Factors that have emerged from the literature are organized in a theoretical framework that links social, economic, cultural and political drivers of migration readiness, willingness and ability in response to slow and fast onset climate events. From a theoretical perspective, it turns out not to be so clear that climate change must lead to more people being on the run, as some of the drivers have diverging and sometimes opposite effects on readiness, willingness or ability. The paper concludes with an outlook for the uncertain future impacts of climate change on migration flows.