A great paradox in cellular immunology is how T cell allorecognition exists at high frequencies (up to 10%) despite the stringent requirements of discriminating 'self' from 'non-self' imposed by MHC restriction. Thus, in tissue transplantation, a substantial proportion of the recipient's T cells will have the ability to recognize the graft and instigate an immune response against the transplanted tissue, ultimately resulting in graft rejection--a manifestation of T cell alloreactivity. Transplantation of human organs and lymphoid cells as treatment for otherwise life-threatening diseases has become a more routine medical procedure making this problem of great importance. Immunologists have gained important insights into the mechanisms of T cell alloreactivity from cytotoxic T cell assays, affinity-avidity studies, and crystal structures of peptide-MHC (pMHC) molecules and T cell receptors (TCRs) both alone and in complex. Despite the clinical significance of alloreactivity, the crystal structure of an alloreactive human TCR in complex with both cognate pMHC and an allogeneic pMHC complex has yet to be determined. This review highlights some of the important findings from studies characterizing the way in which alloreactive T cell receptors and pMHC molecules interact in an attempt to resolve this great irony of the cellular immune response.