Crystal structures of 11 complexes of TCRs with peptide/MHC (pMHC), that represent 6 independent TCRs, constitute the current structural database for deriving general insights into how αβ TCRs recognise peptide-bound MHC class I or class II. The TCRs adopt a roughly diagonal orientation on top of the pMHCs, but the identification of a set of conserved interactions that dictate this orientation is not apparent. Furthermore, the specific interaction of each TCR with its cognate pMHC partner is quite variable and also involves bound water molecules at the TCR/pMHC interface. In two of the systems, the structural basis for binding of altered peptide ligands has illustrated that the only significant conformational changes occur in the TCR/pMHC interface, but their small magnitude is inconsistent with the enormous variation in signalling outcomes. The TCRs adjust to different agonist, partial agonist and antagonist peptides by subtle conformational changes in their complementarity-determining regions, as previously observed in induced-fit mechanisms of antibody/antigen recognition. Alloreactive-complex structures determined or modelled so far indicate increased interactions of the TCR β-chain with the pMHC compared with their syngeneic counterparts.