Over the past several decades, increasingly sophisticated models of the heart have provided important insights into cardiac physiology and are increasingly used to predict the impact of diseases and therapies on the heart. In an era of personalized medicine, many envision patient-specific computational models as a powerful tool for personalizing therapy. Yet the complexity of current models poses important challenges, including identifying model parameters and completing calculations quickly enough for routine clinical use. We propose that early clinical successes are likely to arise from an alternative approach: relatively simple, fast, phenomenologic models with a small number of parameters that can be easily (and automatically) customized. We discuss examples of simple yet foundational models that have already made a tremendous impact on clinical education and practice, and make the case that reducing rather than increasing model complexity may be the key to realizing the promise of patient-specific modeling for clinical applications.