© 2016 by the authors.Climate change is one of the greatest threats to the persistence of coral reefs. Sustained and ongoing increases in ocean temperatures and acidification are altering the structure and function of reefs globally. Here, we summarise recent advances in our understanding of the effects of climate change on scleractinian corals and reef fish. Although there is considerable among-species variability in responses to increasing temperature and seawater chemistry, changing temperature regimes are likely to have the greatest influence on the structure of coral and fish assemblages, at least over short-medium timeframes. Recent evidence of increases in coral bleaching thresholds, local genetic adaptation and inheritance of heat tolerance suggest that coral populations may have some capacity to respond to warming, although the extent to which these changes can keep pace with changing environmental conditions is unknown. For coral reef fishes, current evidence indicates increasing seawater temperature will be a major determinant of future assemblages, through both habitat degradation and direct effects on physiology and behaviour. The effects of climate change are, however, being compounded by a range of anthropogenic disturbances, which may undermine the capacity of coral reef organisms to acclimate and/or adapt to specific changes in environmental conditions.