Vertebrate hemoglobins are tetramers made of two pairs of alpha and beta subunits each containing a hydrophobic pocket where a heme molecule binds tightly and allows for the reversible binding of oxygen. Both tertiary and quaternary structures are ideally suited for the loading and unloading of oxygen necessary for the metabolic requirements of the organisms. Starting from a single ancestor hemoglobin subunit, evolutionary processes have led to heterologous tetramers exhibiting a moderate oxygen affinity due to heme-heme interaction (allosteric mechanism) which may be further modulated through electrostatic interactions with chloride and/or organophosphate anions present in the red cells. These effectors, which bind preferentially to the deoxy-Hb tetramers at a distance from the heme groups, play a major role in the adaptation of the respiratory properties of hemoglobin to either allometric-dependent oxygen needs or to various hypoxic environments such as altitude, burrowing, or foetal life. In most cases the existence or the strength of the effector-Hb complexes, hence the changes in the allosteric equilibrium, may be ascribed to one or a few mutations of residues at the effector binding sites. Typical examples of these mechanisms are described.