Organ transplantation has evolved over the past 30 years, although 'new' and 'old' problems remain unsolved, which from a personal point of view, might be summarized as: i) the transfusion effect; ii) HLA matching and pre-graft sensitization of the potential recipient; iii) immunosuppressive drugs; iv) the pathogenesis of chronic rejection; v) infections; vi) de novo cancers. The aim is to attain a state of specific immunological tolerance without the use of immunosuppressive drugs.