The absolute values of the O2-affinities (P50, Klow, and Khigh) of hemoglobin (Hb) are regulated neither by changes in the static T-/R-quaternary and associated tertiary structures nor the ligation states. They are pre-determined and regulated by the extrinsic environmental factors such as pH, buffers, and heterotropic effectors. The effect and role of O2 on Hb are reversibly to drive the structural allosteric equilibrium between the T(deoxy)- and R(oxy)-Hb toward R(oxy)-Hb (the structural allostery). R(oxy)-Hb has a higher O2-affinity (Khigh) relative to that (Klow) of the T(deoxy)-Hb (Khigh>Klow) under any fixed environmental conditions. The apparent O2-affinity of Hb is high, as the globin matrix interferes with the dissociation process of O2, forcing the dissociated O2 geminately to re-bind to the heme Fe. This artificially increases [oxy-Hb] and concomitantly decreases [deoxy-Hb], leading to the apparent increases of the O2-affinity of Hb. The effector-linked high-frequency thermal fluctuations of the globin matrix act as a gating mechanism to modulate such physical, energetic, and kinetic barriers to enhance the dissociation process of O2, resulted in increases in [deoxy-Hb] and concomitant decrease in [oxy-Hb], leading to apparent reductions of the O2-affinity of Hb (the entropic allostery). The heme in Hb is simply a low-affinity O2-trap, the coordination structure of which is not altered by static T-/R-quaternary and associated tertiary structural changes of Hb. Thus, heterotrophic effectors are the signal molecule, which acts as a functional link between these two allosteries and generates the diverse functionality of Hb of physiological relevance. This article is part of a Special Issue entitled: Oxygen Binding and Sensing Proteins.