A mass of experimental data has been accumulated in the 65 years since Hartridge and Roughton made the first measurement of the rapid reaction of haemoglobin with O2 in solution on a millisecond time scale, at first by flow-mixing methods, and, for 30 years or so, by flash photolysis. Technical advances, particularly in lasers, have allowed increasingly rapid reactions to be followed and the fastest reactions now observed have half-times conveniently measured in pico-seconds. The measurements were used at first to discuss the physiology of gas transport and to describe co-operativity in haemoglobin. More recently, the process of ligand binding has been dissected into intramolecular and intermolecular components. Relating the various rates to the abundance of structural information on crystals is so difficult that the work has barely begun, but the combination of kinetic measurements with genetic engineering and crystallography has promise, as well as problems, for the future.