Antibody and T-cell receptor (TCR) molecules may be regarded as products of a protein engineering system for the generation of a virtually unlimited repertoire of complementary molecular surfaces. This extreme structural heterogeneity is required for recognition of the infinite array of antigenic determinants presented in nature. Here we broadly discuss the structures of antibodies and TCRs as well as their specific recognition of antigen, the binding energetics of these interactions, the structural basis of the antibody maturation and TCR selection processes, limitations to affinity and specificity for antigens, and the role of conformational flexibility in antigen recognition. A final section highlights research results from the burgeoning field of natural killer cell receptor biology.