The first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method for electronic structure studies has been applied to a variety of complex inorganic crystals. The theory and the practice of the OLCAO method in the local density approximation are discussed in detail. Recent progress in the study of electronic and optical properties of a large list of ceramic systems are summarized. Eight selected topics on different ceramic crystals focusing on specific points of interest are presented as examples. The materials discussed are AIN, Cu20, p-Si3N4, Y203, LiB305, ferroelectric crystals, Fe-B compounds, and the YBa2Cu307 superconductor. The results include the band structure, density of states, charge density distribution, spin density distribution, effective charges, total energy and totalenergy-derived results, optical absorption, positron annihilation spectra, and more. Extension of the band theoretical approach to the study of other areas of fundamental ceramic science is also discussed. [