Considering the variety of species that depend on hemoglobin for oxygen transport, these molecules must execute their primary function under extreme environmental conditions. Hence, a thermodynamic analysis of oxygen binding with hemoglobins from different species reveals a series of adaptive mechanisms which are based on the thermodynamic connection between the binding of heterotropic effectors and the reaction with oxygen. The examples reported, from fishes to human fetus, illustrate how evolution can alter the structural basis of the heterotropic interactions to optimize the oxygenation-deoxygenation cycle in dependence of the physiological needs of the particular organisms. Moreover they show that a thermodynamic analysis of the reaction with oxygen overcomes the meaning of a detailed structural and functional characterization going deeper into the physiology of the specific organism.