The knowledge of the interaction between oxygen (O2) and hemoglobin (Hb) is essential both for understanding oxygen transport phenomena and for testing theories of protein structure and function. The equilibrium reaction is measured routinely simply to estimate the position and shape of the O2-binding curve from, respectively, the O2 pressure at half saturation (P50) and the index of cooperativity (i.e., the Hill number, n), but thermodynamic analysis of individual binding steps is more difficult because of inherent complexities in the reaction. The Hb conformational transition is another area under study. Strong allosteric effectors, such as inositol hexaphosphate and bezafibrate, are being used to test this by possibly enhancing the signal. In the future, mathematical models will include calculations of tetramer dissociation and subunit differences in ligand binding. As instruments and theory improve, the critical components of the reaction will be resolved better and, once limiting assumptions are no longer required for experimental analyses, the evaluation of Hb-O2 equilibrium binding will become a simpler and more reliable process.