Anthropogenic sea-level rise (SLR) is predicted to impact, and, in many cases, displace, a large proportion of the population via inundation and heightened SLR-related hazards. With the global coastal population projected to surpass one billion people this century, SLR might be among the most costly and permanent future consequences of climate change. In this Review, we synthesize the rapidly expanding knowledge of human mobility and migration responses to SLR, providing a coherent roadmap for future SLR research and associated policy. While it is often assumed that direct inundation forces a migration, we discuss how mobility responses are instead driven by a diversity of socioeconomic and demographic factors, which, in some cases, do not result in a migration response. We link SLR hazards with potential mechanisms of migration and the associated governmental or institutional policies that operate as obstacles or facilitators for that migration. Specific examples from the USA, Bangladesh and atoll island nations are used to contextualize these concepts. However, further research is needed on the fundamental mechanisms underlying SLR migration, tipping points, thresholds and feedbacks, risk perception and migration to fully understand migration responses to SLR.