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Hemoglobin and myoglobin have been considered for a long time the paradigmatic model systems for protein function, to the point of being defined the “hydrogen atom[s] of biology” [Frauenfelder et al. Proc. Natl. Acad. Sci. USA, 2003; 100, 8615-8617]. Given this privileged position and the huge amount of quantitative information available on these proteins, the red blood cell might appear as the model system and“hydrogen atom” of system biology. Indeed, since the red cell's main function is O2 transport by hemoglobin, the gap between the protein and the may appear quite small. Yet, a surprisingly large amount of detailed biochemical information is required for the modellization of the respiratory properties of the erythrocyte. This problem is compounded if modellization aims at uncovering or explaining evolutionarily selected functional properties of hemoglobin. The foremost difficulty lies in the fact that hemoglobins having different intrinsic properties and relatively ancient evolutionary divergence may behave similarly in the complex milieu of blood, whereas very similar hemoglobins sharing a substantial sequence similarity may present important functional differences because of the mutation of a few key residues. Thus the functional properties of hemoglobin and blood may reflect more closely the recent environmental challenges than the remote evolutionary history of the animal. We summarize in this review the case of hemoglobins from mammals, in an attempt to provide a reasoned summary of their complexity that, we hope, may be of help to scientists interested in the quantitative exploration of the evolutionary physiology of respiration. Indeed the basis of a meaningful modellization of the red cell requires a large amount of information collected in painstaking and often forgotten studies of the biochemical properties of hemoglobin carried out over more than a century.