The artificial transfer of tissues or cells between genetically diverse individuals elicits an immune response that is adaptive and specific. This response is orchestrated by T lymphocytes that are recognizing, amongst others, major histocompatibility complex (MHC) molecules expressed on the surface of the transferred cells. Three pathways of recognition are described: direct, indirect and semi-direct. The sets of antigens that are recognized in this setting are also discussed, namely, MHC protein products, the MHC class I-related chain (MIC) system, minor histocompatibility antigens and natural killer cell receptor ligands. The end product of the effector responses are hyperacute, acute and chronic rejection. Special circumstances surround the situation of pregnancy and bone marrow transplantation because in the latter, the transferred cells are the ones originating the immune response, not the host. As the understanding of these processes improves, the ability to generate clinically viable immunotherapies will increase.