This mini-review, mainly based on our resonance Raman studies on the structural origin of cooperative O binding in human adult hemoglobin (HbA), aims to answering why HbA is a tetramer consisting of two α and two β subunits. Here, we focus on the Fe-His bond, the sole coordination bond connecting heme to a globin. The Fe-His stretching frequencies reflect the O affinity and also the magnitude of strain imposed through globin by inter-subunit interactions, which is the origin of cooperativity. Cooperativity was first explained by Monod, Wyman, and Changeux, referred to as the MWC theory, but later explained by the two tertiary states (TTS) theory. Here, we related the higher-order structures of globin observed mainly by vibrational spectroscopy to the MWC theory. It became clear from the recent spectroscopic studies, X-ray crystallographic analysis, and mutagenesis experiments that the Fe-His bonds exhibit different roles between the α and β subunits. The absence of the Fe-His bond in the α subunit in some mutant and artificial Hbs inhibits T to R quaternary structural change upon O binding. However, its absence from the β subunit in mutant and artificial Hbs simply enhances the O affinity of the α subunit. Accordingly, the inter-subunit interactions between α and β subunits are nonsymmetric but substantial for HbA to perform cooperative O binding.