40 years after introduction of the Fontan operation there are a lot of doubts regarding the treatment strategy for patients with a single ventricle. With the progress in medical science, the number of patients with a univentricular heart is steadily growing, and growing at the same time is the population of patients who do not tolerate the Fontan haemodynamics. In this group with time there occurs impairment of ventricular function and heart failure, regurgitation of the atrioventricular valves, protein-losing enteropathy, hepatic failure, progressive cyanosis, thromboembolic complications, development of fistulas in the lungs and arrhythmias. If the causes of complications are anatomical problems or arrhythmias, which are possible to repair, reoperation or intervention may improve the condition of the patient. However, there is a group of patients where the only real option is a cardiac transplantation. Heart transplantation after the Fontan operation is technically difficult and requires coordination of many activities. Another option, which is currently in the experimental stage, is implantation of a mechanical assist system in the Fontan circulation (cavopulmonary assist), to reverse the so-called “Fontan paradox”.