Tetrameric haemoglobins display a cooperative ligand binding behaviour, which has been attributed to the functional interrelationship between multiple ligand binding sites. The quantitative description of this feature was initially carried out with a phenomenological approach, which was limited to the functional effect of the occupancy by a ligand molecule of a binding site on further binding steps. However, subsequent development of structural-functional models for the description of the cooperativity in haemoglobin brought about a much deeper information on the interrelationships between ligand binding at the heme and structural variations occurring in the surrounding free subunits. This approach opened the way to the evolution of the concept of allostery, which is intended as the structural-functional effect exerted by the presence of a ligand in a binding site on other binding sites present in the same molecule. This concept can be applied to either sites for the same ligand (homotropic allostery) and for sites of different ligands (heterotropic allostery). Several models trying to take into account the continuous building up of structural and functional information on the physicochemical properties of haemoglobin have been developed along this line.