Neonatal heart transplantation was developed and established in the 1980's as a durable modality of therapy for complex-uncorrectable heart disease. Patients transplanted in the neonatal period have experienced unparalleled long-term survival, better than for any other form of solid-organ transplantation. However, the limited availability of neonatal and young infant donors has restricted the indications and applicability of heart transplantation among newborns in the current era. Indications for heart transplantation include congenital heart disease not amenable to other forms of surgical palliation, and cardiomyopathy, including some primary tumors. Use of ABO-incompatible transplants, and organs with prolonged cold ischemic time or marginal function have all been associated with good outcomes in infants. These extended strategies to increase the donor pool may also someday include donation after determination of circulatory death and the use of anencephalic donors. The operative techniques for donors and recipients of neonatal heart transplantation are unique and have been well-described. Immunosuppression protocols for neonates need not include induction and are largely steroid-free. Newborn and young infant transplant recipients have fewer episodes of rejection, less coronary allograft vasculopathy, less post-transplant lymphoproliferative disease and less renal dysfunction than their older counterparts. Long-term outcomes have been very encouraging in terms of graft survival, patient survival, and quality of life. Our review highlights the history, current indications, techniques and outcomes of heart transplantation in this immunologically-privileged subset of patients.