Organ transplantation has been the most important therapeutic advance in the last third of the 20th century. Its development has revolutionized medicine, as demonstrated by the fact that a large number of researchers in this field have been awarded Nobel Prizes. In the beginning of this century, we are witnessing with great expectations the emergence of a new field of medicine related to the arrival of a new player on the scene: stem cells and their potential use in regenerative medicine. This volume aims to cover important aspects of the various facets of organ transplantation and regenerative medicine, with leading specialists in these fields setting out their vision. We try to rigorously explain current and novel scientific research in these fieldsareas which arouse great interest from society in general, due to their potential use in modern medicine for the treatment of a great number of diseases.