Allostery arises when a ligand-induced change in shape of a binding site of a protein is coupled to a tertiary/quaternary conformational change with a consequent modulation of functional properties. The two-state allosteric model of Monod, Wyman and Changeux [J. Mol. Biol. 1965; 12, 88-118] is an elegant and effective theory to account for protein regulation and control. Tetrameric hemoglobin (Hb), the oxygen transporter of all vertebrates, has been for decades the ideal system to test for the validity of the MWC theory. The small ligands affecting Hb's behavior (organic phosphates, protons, bicarbonate) are produced by the red blood cell during metabolism. By binding to specific sites, these messengers make Hb sensing the environment and reacting consequently. HbI and HbIV from trout and human HbA are classical cooperative models, being similar yet different. They share many fundamental features, starting with the globin fold and the quaternary assembly, and reversible cooperative O2 binding. Nevertheless, they differ in ligand affinity, binding of allosteric effectors, and stability of the quaternary assembly. Here, we recollect essential functional properties and correlate them to the tertiary and quaternary structures available in the protein databank to infer on the molecular basis of the evolution of oxygen transporters.