Climate change is driving changes in the physical and chemical properties of the ocean that have consequences for marine ecosystems. Here, we review evidence for the responses of marine life to recent climate change across ocean regions, from tropical seas to polar oceans. We consider observed changes in calcification rates, demography, abundance, distribution and phenology of marine species. We draw on a database of observed climate change impacts on marine species, supplemented with evidence in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. We discuss factors that limit or facilitate species’ responses, such as fishing pressure, the availability of prey, habitat, light and other resources, and dispersal by ocean currents. We find that general trends in species responses are consistent with expectations from climate change, including poleward and deeper distributional shifts, advances in spring phenology, declines in calcification and increases in the abundance of warm-water species. The volume and type of evidence of species responses to climate change is variable across ocean regions and taxonomic groups, with much evidence derived from the heavily-studied north Atlantic Ocean. Most investigations of marine biological impacts of climate change are of the impacts of changing temperature, with few observations of effects of changing oxygen, wave climate, precipitation (coastal waters) or ocean acidification. Observations of species responses that have been linked to anthropogenic climate change are widespread, but are still lacking for some taxonomic groups (e.g., phytoplankton, benthic invertebrates, marine mammals).