The resilience of Caribbean coral reefs, which are an important source of biodiversity and provide essential ecosystem services, is constantly challenged by many reef stressors including ocean acidification, hurricane damage, and overharvesting of herbivorous reef fish. The presence of two alternative stable states—a desirable state with high levels of coral cover and its coral-depleted counterpart—has been widely documented in the literature. Increasing coral resilience to prevent phase shifts to the undesirable state is a critical research priority, and mathematical models can serve as an important tool to not only better understand the underlying dynamics of observed coral communities, but also to evaluate the potential impacts of stressors and the outcome of management strategies designed to promote coral persistence. Here, we review the existing literature of mathematical models designed to understand the processes that generate alternative stable states. We focus on models that are comprised of ordinary differential equations and, at their core, capture algal–coral dynamics. Recommendations for Resource Managers Evidence for the existence of alternative stable states and the associated presence of hysteresis implies a need for management designed to increase the resilience of coral reef ecosystems. In addition, holistic approaches to designing management strategies are required to both increase resilience of coral reefs and maximize the benefits of the ecosystem services they provide. Due to the intrinsic complexity and spatial variability of coral reef ecosystems, management cannot be designed using a “one size fits all” approach. Instead, local dynamics and stressors need to be carefully considered.