According to the classical view of allograft rejection, the transplanted tissue is the source of antigen that stimulates a T-cell response, which in turn sets up the rejection process. Research now indicates that two signals are required for lymphocyte activation. The first signal is provided by antigen binding by the T-cell receptor. A stimulator cell provides an inductive molecule, costimulator activity, which is the second signal. The stimulator cell model of lymphocyte activation has resulted in a new passenger leukocyte concept, in which these passenger cells are seen to play a central role in graft rejection. Appropriate treatment of a tissue prior to transplantation can afford a marked reduction in its immunogenicity for the host. It is now possible to eliminate or at least reduce tissue immunogenicity by removal of leukocytes from the transplant prior to grafting. This phenomenon has been demonstrated to be effective with both endocrine tissue and larger organs, such as the kidney. There is some variation in the effectiveness of the technique with different tissues which can be related to the degree of leukocyte contamination. Ailografts of pretreated tissue can induce a state of specific unresponsiveness in the adult recipient. Although the mechanism of this tolerance is not fully understood, the existence of the phenomenon is one of the most encouraging recent developments in transplantation biology.