One of the great discoveries in cardiac electrophysiology was the recognition of the crucial role of pulmonary vein (PV) myocardial sleeves for the initiation of atrial fibrillation (AF). Based on this concept, catheter ablation aiming at electrical isolation of all pulmonary veins has become the routine approach for of paroxysmal AF. Another concept implies selective isolation only of arrhythmogenic PVs. Based on the most important studies dealing with both approaches, we describe pros and cons of selective compared to complete pulmonary vein isolation (PVI) and illustrate why selective PVI has not found widespread acceptance in the electrophysiologic community.