Tropical fisheries substantially contribute to the well-being of societies in both the tropics and the extratropics, the latter through ‘telecoupling’ — linkages between distant human–natural systems. Tropical marine habitats and fish stocks, however, are vulnerable to the physical and biogeochemical oceanic changes associated with rising greenhouse gases. These changes to fish stocks, and subsequent impacts on fish production, have substantial implications for the UN Sustainable Development Goals. In this Review, we synthesize the effects of climate change on tropical marine fisheries, highlighting the socio-economic impacts to both tropical and extratropical nations, and discuss potential adaptation measures. Driven by ocean warming, acidification, deoxygenation and sea-level rise, the maximum catch potential of tropical fish stocks in some tropical exclusive economic zones is projected to decline by up to 40% by the 2050s under the RCP8.5 emissions scenario, relative to the 2000s. Climate-driven reductions in fisheries production and alterations in fish-species composition will subsequently increase the vulnerability of tropical countries with limited adaptive capacity. Thus, given the billions of people dependent on tropical marine fisheries in some capacity, there is a clear need to account for the effects of climate change on these resources and identify practical adaptations when building climate-resilient sustainable-development pathways.