Three different theoretical considerations are used to probe some of the factors which determine the "complexity" of solids. It is first shown how simple topological restrictions, set by stoichiometry and local coordination number, have an important bearing on the generation of locally symmetric arrangements of atoms. Through the introduction of an orbital picture which provides an electronic underpinning of the valence sum rules of Pauling and Brown, it is shown how the local structure is determined by the electronic configuration. Finally, the use of the method of moments enables comments to be made concerning the identity of nearest-neighbor atoms and linkages of various types as a function of electron count. By study of the behavior of the fourth moment as a function of an order parameter, it is shown how ordered arrangements of atoms and bonds are electronically favored.