Atrial fibrillation (AF) is the most common arrhythmia targeted by catheter ablation. Despite significant advances in our understanding of AF, ablation outcomes remain suboptimal, and this is due in large part to an incomplete understanding of the underlying sustaining mechanisms of AF. Recent developments of patient-tailored and physiology-based computational mapping systems have identified localized electrical spiral waves, or rotors, and focal sources as mechanisms that may represent novel targets for therapy. This report provides an overview of Focal Impulse and Rotor Modulation (FIRM) mapping, which reveals that human AF is often not actually driven by disorganized activity but instead that disorganization is secondary to organized rotors or focal sources. Targeted ablation of such sources alone can eliminate AF and, when added to pulmonary vein isolation, improves long-term outcome compared with conventional ablation alone. Translating mechanistic insights from such patient-tailored mapping is likely to be crucial in achieving the next major advances in personalized medicine for AF.