The structure and bonding in alpha and beta octamolybdate anions have been investigated using density functional methods. In general, good computational-experimental agreement for the geometrical parameters has been obtained. The electronic structure of the anions has been probed with molecular orbital and Mulliken-Mayer methods. All Mo-O interactions have been found to be predominantly d(Mo)-p(O) in character. Several multicentered molecular orbitals can be described as sigma or pi closed-loop structures, but the proposed connection with the stability of the polyanions is not completely supported by the calculations. Mayer indexes correspond to fractional multiple character for terminal bonds and approximately single or low-order character for bridging bonds, in accordance with structural and bond valence results. The valency analysis has yielded similar overall bonding capacity for the various oxygen atoms. A distribution of the negative charge over all types of oxygen sites and metal charges considerably smaller than the formal oxidation states have been obtained from the Mulliken analysis.