A study of structure and bonding in neutral and cationic sodium monoxides NamO (m = 2 - 6) and dioxides NanO2 (n = 1 - 9) is presented. Structural isomers, adiabatic ionization potentials and sodium bond energies are calculated and the factors leading to ＇＇outer shell＇＇ sodium are discussed. Monoxide and superoxide properties are investigated using a range of ab initio methods. Density functional theory (DFT) results are found to compare favorably with those from experiment and from more expensive theoretical approaches. DFT is therefore used for all the dioxide calculations. The dioxides are rationalized in terms of the three oxidation states O-2(-), O-2(2-) and 2O(2-), representing three stages in the odor reaction between sodium and oxygen. Superoxide NaO : may be reduced by sodium to peroxides NanO2 (n = 2 - 4), containing O-2(2-) stabilized by an equatorial Na cage. O-O cleavage occurs when Na attacks apically, releasing charge stored in this cage and effecting a two electron transfer to 2O(2-). The resulting compounds NanO2 (n = 5 - 9) may be understood as sodium-bridged bis-monoxides.