Viruses are ubiquitous members of the coral holobiont and the coral reef ecosystem. They infect coral cells, endosymbionts, prokaryotes, and all reef inhabitants, contributing to their physiology and ecological relationships. Here, we review the current knowledge on the diversity and functions of viruses in corals and coral reefs. We describe the viral groups that are found in most coral viromes and the shifts in the viral community composition associated with environmental stress and disease. Selective lysis of host cells by viruses modulate microbiome composition, and virus-mediated genetic exchange increases genomic flexibility of hosts. Through these mechanisms, viruses may contribute to acclimation and adaptation of coral holobionts, including resilience against temperature stress and protection against pathogens. We also explore how coral reef viruses modulate reef-scale processes such as organic matter turnover, biomass transfers, and biogeochemical cycles. Current data indicate that predation pressure exerts an important control of bacterial biomass and the detrimental microbialization of coral reefs. Finally, we identify challenges in virus research and future directions toward a mechanistic understanding of the role of viruses in coral reefs.