Antigen-specific T-cell responses induced by infection, transplantation, autoimmunity or hypersensitivity are characterized by cells expressing biased profiles of T-cell receptors (TCRs) that are selected from a diverse, naive repertoire. Here, we review the evidence for these TCR biases, focusing on crystallographic analysis of the structural constraints that determine the binding of a TCR to its ligand and the persistence of certain TCRs in an immune repertoire. We discuss the ways in which diversity in a selected TCR repertoire can contribute to protective immunity and the implications of this for vaccine design and immunotherapy.