We review contributions made towards the elucidation of CO and O 2 binding geometries in respiratory proteins. Nuclear magnetic resonance, infrared spectroscopy, Mössbauer spectroscopy, X-ray crystallography and quantum chemistry have all been used to investigate the Fe –ligand interactions. Early experimental results showed linear correlations between 17 O chemical shifts and the infrared stretching frequency (νCO) of the CO ligand in carbonmonoxyheme proteins and between the 17 O chemical shift and the 13CO shift. These correlations led to early theoretical investigations of the vibrational frequency of carbon monoxide and of the 13 C and 17 O NMR chemical shifts in the presence of uniform and non-uniform electric fields. Early success in modeling these spectroscopic observables then led to the use of computational methods, in conjunction with experiment, to evaluate ligand-binding geometries in heme proteins. Density functional theory results are described which predict 57 Fe chemical shifts and Mössbauer electric field gradient tensors, 17 O NMR isotropic chemical shifts, chemical shift tensors and nuclear quadrupole coupling constants (e2qQ/h) as well as 13 C isotropic chemical shifts and chemical shift tensors in organometallic clusters, heme model metalloporphyrins and in metalloproteins. A principal result is that CO in most heme proteins has an essentially linear and untilted geometry (τ = 4 °, β = 7 °) which is in extremely good agreement with a recently published X-ray synchrotron structure. CO / O 2 discrimination is thus attributable to polar interactions with the distal histidine residue, rather than major Fe–C–O geometric distortions.