Neonates with functional single ventricles have pulmonary and systemic circulations that are supplied in parallel, creating significant cyanosis and ventricular volume overload. The goal of palliative surgery, excluding transplantation, is to convert single-ventricle circulation from a parallel to a series arrangement. This will ultimately require a complete cavopulmonary anastomosis (Fontan-type procedure) in which vena caval blood is rerouted directly into the pulmonary circulation. Various factors require that this palliation occur in stages. Stage I surgery, which is often a Norwood procedure, is done in the neonatal period and stabilizes, but does not resolve, parallel circulation. The tenuous balance between pulmonary and systemic perfusion during this stage makes noncardiac surgery hazardous, and it should be restricted to urgent or emergent indications. Stage II surgery, or partial cavopulmonary anastomosis, relieves both parallel circulation and volume overload, but not cyanosis. Relatively stable hemodynamics during this stage create favorable conditions for elective surgery. Patients who have undergone stage III surgery, the Fontan-type repair, vary in age from toddlers to adults, and in physical status from well-compensated to significantly debilitated. Fontan patients require thorough preoperative assessment when elective surgery is contemplated. Optimal communication between surgeons, anesthesiologists, and cardiologists is essential when caring for the patient with single-ventricle physiology.