Congenital coronary artery fistulas are rare anomalies. As coronary angiography and multidetector computed tomography have become more accessible, they have been increasingly used in the investigation of chest pain and heart failure. Coronary artery fistulas are often an incidental finding, which raises the question of how patients with this condition should be managed. Intervention with either transcatheter closure or surgical closure is often technically possible. Many patients are asymptomatic early after closure. However, follow-up studies have shown post-closure sequelae, such as residual leakage, thrombosis with or without myocardial infarction, and coronary stenosis. Therefore, there has been a shift from intervention towards watchful waiting in asymptomatic patients. In this article, we review the published literature on the natural history and treatment outcomes in individuals with coronary artery fistulas. We present case reports from our clinic and discuss the management of incidental findings of coronary artery fistulas.