Antibodies and T-cell receptors (TCRs) are the fundamental building blocks of adaptive immunity. Repertoire-scale functionality derives from their epitope-binding properties, just as macroscopic properties like temperature derive from microscopic molecular properties. However, most approaches to repertoire-scale measurement, including sequence diversity and entropy, are not based on antibody or TCR function in this way. Thus, they potentially overlook key features of immunological function. Here we present a framework that describes repertoires in terms of the epitope-binding properties of their constituent antibodies and TCRs, based on analysis of thousands of antibody-antigen and TCR-peptide-major-histocompatibility-complex binding interactions and over 400 high-throughput repertoires. We show that repertoires consist of loose overlapping classes of antibodies and TCRs with similar binding properties. We demonstrate the potential of this framework to distinguish specific responses vs. bystander activation in influenza vaccinees, stratify CMV-infected cohorts, and identify potential immunological “super-agers.” Classes add a new dimension to assessment of immune function.