The interaction between the T‐cell receptor (TCR) and its peptide–major histocompatibility complex (pepMHC) ligand plays a critical role in determining the activity and specificity of the T cell. The binding properties associated with these interactions have now been studied in many systems, providing a framework for a mechanistic understanding of the initial events that govern T‐cell function. There have been various other reviews that have described the structural and biochemical features of TCR : pepMHC interactions. Here we provide an overview of four areas that directly impact our understanding of T‐cell function, as viewed from the perspective of the TCR : pepMHC interaction: (1) relationships between T‐cell activity and TCR : pepMHC binding parameters, (2) TCR affinity, avidity and clustering, (3) influence of coreceptors on pepMHC binding by TCRs and T‐cell activity, and (4) impact of TCR binding affinity on antigenic peptide specificity.