Corals provide the foundation of important tropical reef ecosystems but are in global decline for multiple reasons, including climate change. Coral health depends on a fragile partnership with intracellular dinoflagellate symbionts. We argue here that progress in understanding coral biology requires intensive study of the cellular processes underlying this symbiosis. Such study will inform us on how the coral symbiosis will be affected by climate change, mechanisms driving coral bleaching and disease, and the coevolution of this symbiosis in the context of other host-microbe interactions. Drawing lessons from the broader history of molecular and cell biology and the study of other host-microbe interactions, we argue that a model-systems approach is essential for making effective progress in understanding coral cell biology.