While major improvements have been made in the prevention and treatment of hyperacute and acute transplant rejection, most grafts will succumb to chronic rejection: this reflects the extent of our knowledge of the mechanisms that drive these processes. Clinically, transplant rejection is classified according to timeframe and histology into hyperacute (minutes to hours), acute (days to months) and chronic rejection (months to years). Hyperacute and acute rejection are reasonably well understood and occur by immune mediated events whereas chronic rejection probably has immune and non-immune components. The trigger to cell-mediated rejection is allorecognition, where same-species, non-self antigens are detected by the host immune system. This occurs by two distinct mechanisms, called the direct and indirect pathways. The direct pathway results from the recognition of foreign major histocompatibility molecules, intact, on the surface of donor cells. Indirect allorecognition occurs when donor histocompatibility molecules are internalised, processed, and presented as peptides by host antigen presenting cells. Animal and human studies strongly suggest that acute rejection is predominantly triggered by the direct pathway although if the latter is blocked then the indirect pathway can suffice. Donor antigen presenting cells within the graft become depleted with time and the frequency of T cells reactive to the direct pathway diminishes irrespective of whether or not chronic rejection occurs. This implies that the direct pathway is unlikely to contribute to chronic rejection. Assays of T cell responses have, however, found an association between the indirect pathway and chronic rejection although it is unlikely that this is the whole story: there are numerous non-immunological risk factors for chronic rejection which probably interact with immune components causing gradual graft failure. Xenotransplantation, where tissue is transferred across species, causes rejection by processes analogous to those seen in allografts but they are faster and more vigorous. Novel approaches have overcome some early antibody mediated rejection events but then reveal a huge, intense, adaptive cellular response. We believe that by the careful study of the mechanisms of rejection, the problems of chronic rejection and xenograft rejection will be overcome, thus reversing the widening gap between organ demand and supply.