Against the background of potentially substantial sea-level rise, one important question is to what extent are coastal societies able to adapt? This question is often answered in the negative by referring to sinking islands and submerged megacities. Although these risks are real, the picture is incomplete because it lacks consideration of adaptation. This Perspective explores societies' abilities to adapt to twenty-first-century sea-level rise by integrating perspectives from coastal engineering, economics, finance and social sciences, and provides a comparative analysis of a set of cases that vary in terms of technological limits, economic and financial barriers to adaptation and social conflicts.