A description of electronic structures of polyatomic molecules in terms of atomic and molecular orbitals (one-electron orbital wave functions) is suggested, as follows. Unshared electrons are considered as occupying atomic orbitals associated with the various nuclei to which the electrons belong. Shared electrons are described from several points of view, whose simultaneous consideration should give a better understanding of their condition and functions in the molecule. In the first place, they are described, in terms of atomic orbitals, from the point of view of each nucleus in the molecule. In the second place, they are described from a unitary molecular point of view, in terms of molecular orbitals. It is pointed out that the chemical evidence which led Lewis to his concept of the electron-pair bond can now all be explained by the quantum theory without the necessity of using such a concept. It is noted that the Heitler-London, Pauling-Slater quantum-mechanical electron-pair bond concept differs markedly from Lewis's, also that it is of more restricted application to chemical data. It is pointed out, in agreement with Hund, that properties of the H. and L., S. and P. electron-pair bond which make it useful in dealing with chemical combination are also prossessed by the concept of molecular orbitals. For example, the Pauling-Slater criterion that bonds which correspond to a maximum overlapping of atomic orbitals are the strongest is just as characteristic of bonding molecular orbitals as of electron-pair bonds. An electron-pair bond is here interpreted as being little other than two electrons occupying a bonding molecular orbital. Or in general one must say that a set of n electron-pair bonds is interpreted as a set of 2n electrons occupying n molecular orbitals, because molecular orbitals are not necessarily localized between two nuclei like electron-pair bonds. It is concluded that the essential facts of molecular electronic structure can be qualitatively understood in terms of the mode of description stated in the first paragraph above and of a semi-empirical valence rule (not essentially new) which summarizes, in the light of quantum theory, the most important regularities in regard to the types of chemical compounds which are stable.