After more than a century of experimental, theoretical and computational studies, there is no general agreement yet on the mechanisms underlying the fine regulation of hemoglobin structural and functional properties. The experiments that we have carried out during the last two decades on hemoglobin immobilized in the crystal or in nanoporous silica gels have demonstrated that oxygen binding to a single quaternary structure is non-cooperative. This work finally settled the controversy among competing allosteric models. In addition, a vast amount of experimental evidence has been accumulated showing that tertiary conformational changes play a major role in the functional regulation of hemoglobin, even within a single quaternary state, an observation that is inconsistent with the classical MWC model. Experiments appear to be fully consistent with the Tertiary Two State allosteric model, recently proposed by Eaton and co-workers. The theoretical and experimental approaches described in this review should help in providing a quantitative understanding of allosteric interactions in other multi-subunit protein complexes.