The goal of this presentation is to review recent non-invasive imaging- and simulation-based strategies aimed at improving the diagnosis and treatment of patients with arrhythmias and structural heart disease. These strategies entail the creation of a virtual replica of the electrical function of the patient’s heart (a virtual heart). The entails creating a personalized geometrical model of ventricular structure based on the distribution of structural remodeling in the patient ventricles as obtained from clinical scans, and on the biology and physics of heart cells and the electrical current flow through the cardiac syncytium. Using a virtual heart, the patient’s unique lethal heart rhythm disorder can be studied, and personalized treatment devised. We present the fundamentals of the methodology, including image processing techniques, fiber orientation estimation, mesh generation, and detail regarding electrophysiological modeling. We outline important assumptions and limitations, and provide a review of validation studies. We then present recent applications of the personalized virtual-heart approach in predicting the optimal targets for infarct-related ventricular tachycardia ablation and in determining risk of sudden cardiac death in myocardial infarction patients, emphasizing the potential advantages of the approach in comparison to the current standard of care. We discuss the potential impact this approach could have on treatments for heart rhythm disorders and how that can bring precision medicine to the arena of cardiac care. The hope is that with such models at the patient bedside, therapies could be improved, invasiveness of diagnostic procedures minimized, and health-care costs reduced.