Since 1971, the Fontan operation has been performed for the repair of single-ventricle physiology. This ingenious operation commits a single ventricle to the systemic circulation and takes advantage of cardiovascular and respiratory physiology to propel deoxygenated blood to the lungs, thus minimizing right-to-left shunting and cyanosis. Initially performed as a right atrial to pulmonary artery anastomosis, the Fontan operation has gone through evolutionary steps that have resulted in progressive improvements in mortality, morbidity, and outcomes. Inclusion of the right atrium in the slow-flowing Fontan circuit results in progressive dilation and incessant arrhythmias. This spurred forth efforts to create modifications that partially or completely exclude the atrium from the Fontan circuit. The transcatheter completion of the Fontan operation has been performed in a small number of patients and we expect minimally invasive, transcatheter, and hybrid interventions to play an important role in the future management of these patients.