Coral reefs occur in nutrient-poor shallow waters, constitute biodiversity and productivity hotspots, and are threatened by anthropogenic disturbance. This Review provides an introduction to coral reef virology and emphasizes the links between viruses, coral mortality and reef ecosystem decline. We describe the distinctive benthic-associated and water-column- associated viromes that are unique to coral reefs, which have received less attention than viruses in open-ocean systems. We hypothesize that viruses of bacteria and eukaryotes dynamically interact with their hosts in the water column and with scleractinian (stony) corals to influence microbial community dynamics, coral bleaching and disease, and reef biogeochemical cycling. Last, we outline how marine viruses are an integral part of the reef system and suggest that the influence of viruses on reef function is an essential component of these globally important environments.