The human mayor histocompatibility complex class I molecule HLA-A2 preferentially binds peptides that contain Leu at P2 and Val or Leu at the C terminus. The other amino acids in the peptide also contribute to binding positively or negatively. It is possible to estimate the binding stability of HLA-A2 complexes containing particular peptides by applying coefficients, deduced from a large amount of binding data, that quantify the relative contribution of each amino acid at each position. In this review, we describe the molecular basis for these coefficients and demonstrate that estimates of binding stability based on the coefficients are generally concordant with experimental measurements of binding affinities. Peptides that contained cysteine were predicted less well, possibly because of complications resulting from peptide dimerization and oxidation. Apparently, peptide binding affinity is largely controlled by the rate of dissociation of the HLA/peptide/beta 2-microglobulin complex, whereas the rate of formation of the complex has less impact on peptide affinity. Although peptides that bind tightly to HLA-A2, including many antigenic peptides bind much more weakly. Therefore, a full understanding of why certain peptides are immunodominant will require further research.