Cardiovascular medicine focuses on organ and system-scale manifestations of biological processes that can occur at any biological scale, from genetic defects to large-scale injuries. Multiscale models can potentially advance the management of cardiovascular disease by providing predictions of the acute and long-term outcomes of medical devices and treatments. Electrophysiology, hemodynamics, tissue mechanics, and remodeling are the physiological processes most relevant to modeling cardiac function, its ailments, and treatments. Due to their complexity, models of cardiac medical treatment necessitate the strategical allocation of resources to the processes most relevant to pathology and intervention. We review recent developments in multiphysics-multiscale modeling of treatments for hypertension, valvular disease, arrhythmia and dyssynchrony, cardiomyopathy, and heart failure. We emphasize the choices and tradeoffs in these models regarding the level of detail and complexity employed to represent various processes at different scales and the impact of those choices on the ability to predict the effect of treatments, including drug therapy, surgical interventions, resynchronization therapy, and ventricular assist devices.