The status of "partial" tolerance to organ allografts versus the status of complete tolerance is the main topic of this paper. Progress made in immunosuppression, particularly by use of various lymphocyte depleting agents for "induction therapy", seems to favor the subsequent development of T cells with suppressor/regulatory properties. The effective deletion of alloreactive T helper and cytotoxic cells in conjunction with the expansion of antigen-specific suppressor (CD8 + CD28 - FOXP3+) and regulatory (CD4 + CD25+ FOXP3+) T cells creates a milieu in which the graft is well tolerated under an "umbrella" of low dosage immunosuppression. The most effective induction treatment is Campath-1H, although ATGAM at high dosage is also widely used. Total lymphoid irradiation (TLI) is another very effective pretreatment strategy in spite of the risks which are associated with it. The induction of "partial" tolerance is a step in the right direction for exploring strategies that may lead to the induction of complete tolerance. It is safe for the patients and can prolong significantly the function of the graft, preventing the onset of chronic rejection.