More than a decade after the first description of the primary structure of a T-cell antigen receptor (TCR), the recent determination of the crystal structure of several unliganded TCR ectodomains and of two TCRs complexed to peptide-MHC ligand provides a structural basis for understanding the initial event that triggers T-cell activation. This review focuses on the topology of the variable (V) domains found in TCRs and immunoglobulins and attempts to delineate the structural features that may render the TCR complementarity-determining regions particularly suited to dock on the peptide/MHC surface. Finally, the available TCR structures provide an opportunity to re-evaluate the molecular basis for intrathymic positive selection as well as the mechanisms that make a given TCR neither infinitely specific, nor so flexible that it engages productively any MHC-binding peptides.