Liver transplantation has become the best treatment option for cirrhosis, acute liver failure and some tumors. The great advances of recent years have yielded very good results in the long-term survival of these patients. The main complications that occur are vascular and bile duct alterations in the liver graft, relapses of the underlying disease, renal failure, opportunistic infections, and in the long term development of metabolic syndrome, cardiovascular disease, and new malignancies. Currently, several highly complex medical centers in this country perform liver transplants. For this reason it is important for scientists to know the most important aspects in the care of these patients.