The cardinal problem that presents itself when one surveys the impressive amount of data available for the structure of the hemoglobin molecule is, of course, how such a bewilderingly complex arrangement can account for the functions of this protein. The combined results of the X-ray crystallographers ( Perutz et al., 1960 ; Cullis, Muirhead, Perutz, Rossmann & North, 1962 ) and the organic chemists ( Braunitzer et al., 1961 ; Konigsberg, Guidotti & Hill, 1961 ; Braunitzer & Matsuda, 1961 ) have given us considerable information concerning the three-dimensional arrangements, not only of the hemes, but also of the polypeptide chains and, to an increasing extent, even the amino acid residues in the individual chains. The functional integrity of the haemoglobin molecule can be gauged from a number of criteria, all of which stem from its ability to combine reversibly with oxygen. However, in order to qualify as a physiologically useful oxygen carrier, a number of additional closely related properties must be within normal range. The most important of these are the oxygen affinity, the heme-heme interaction, the Bohr effect and the CO2 binding capacity.