The T-cell coreceptors CD4 and CD8 have well-characterized and essential roles in thymic development, but how they contribute to immune responses in the periphery is unclear. Coreceptors strengthen T-cell responses by many orders of magnitude - beyond a million-fold according to some estimates - but the mechanisms underlying these effects are still debated. T-cell receptor (TCR) triggering is initiated by the binding of the TCR to peptide-loaded major histocompatibility complex (pMHC) molecules on the surfaces of other cells. CD4 and CD8 are the only T-cell proteins that bind to the same pMHC ligand as the TCR, and can directly associate with the TCR-phosphorylating kinase Lck. At least three mechanisms have been proposed to explain how coreceptors so profoundly amplify TCR signaling: (1) the Lck recruitment model and (2) the pseudodimer model, both invoked to explain receptor triggering per se, and (3) two-step coreceptor recruitment to partially triggered TCRs leading to signal amplification. More recently it has been suggested that, in addition to initiating or augmenting TCR signaling, coreceptors effect antigen discrimination. But how can any of this be reconciled with TCR signaling occurring in the absence of CD4 or CD8, and with their interactions with pMHC being among the weakest specific protein-protein interactions ever described? Here, we review each theory of coreceptor function in light of the latest structural, biochemical, and functional data. We conclude that the oldest ideas are probably still the best, i.e., that their weak binding to MHC proteins and efficient association with Lck allow coreceptors to amplify weak incipient triggering of the TCR, without comprising TCR specificity.