The strength of the immune response to foreign histocompatibility molecules has long puzzled immunologists. In this article Robert Lechler and colleagues propose that (1) allorecognition is structurally heterogeneous and varies according to the responder and stimulator MHC types, (2) in closely related combinations the focus of the alloreactive T cell may be on epitopes of endogenous peptides that are displayed by stimulator but not by responder MHC molecules, seen in a 'self-restricted' manner, and (3) in more disparate combinations the alloresponse may be directed primarily against residues on the allogeneic MHC molecule itself.