Spectroscopic and chemical evidence speak in favour of the iron--oxygen bond being polar. X-ray analysis shows that the oxygen molecule is inclined at an angle of about 115 degrees to the haem plane. Cooperative binding of oxygen by haemoglobin is due to an equilibrium between two alternative structures, which differ in oxygen affinity by the equivalent of 3-3.5 kcal/mol. I proposed that in the low affinity structure the globin opposes the movement of the iron atom from its five-coordinated pyramidal geometry in the haem of deoxyhaemoglobin to its six-coordinated planar geometry in the haem of oxyhaemoglobin, while in the high affinity structure this restraint is absent. Recent evidence supporting this mechanism is described.