Historically, exogenous administration of hemoglobin solutions to implement the oxygen transport capacity for clinical applications suffered from dramatic drawbacks, resulting in the failure of many attempts. In the last decades, the biochemical and physiological basis responsible for the therapeutic failures has been extensively investigated. It is now widely accepted that they mostly arise because, out of the confined and controlled environment of the red blood cell, hemoglobin exhibits tetramer instability, increased auto-oxidation rate, higher oxygen affinity, altered cooperativity and nitric oxide reactivity. Moreover, it became evident that the design of a hemoglobin-based oxygen carrier that exactly reproduces the "physiological" oxygen-binding curve is not only an overly ambitious task, but may also represent a wrong approach for many potential clinical applications. Under these premises, and given the complex chemical nature of blood, it is obvious that any strategy undertaken to modify the stability and function of the hemoglobin tetramer for clinical use should be driven by a detailed knowledge of its structure, dynamics and mechanism of allosteric regulation. We briefly review the most recent theories and experiments that increased our understanding of the mechanism of homo- and heterotropic effects in human hemoglobin, trying to interpret, on a biophysical basis, how diverse approaches like polymerization, cross-linking, site-directed mutagenesis, surface decoration and encapsulation may affect ligand affinity and allosteric regulation.