Perovskite and perovskite-related structures are important crystallographic structures particularly for oxide functional materials because most of the newly discovered functional materials belong to this category (for a complete list of perovskite structures, see Galasso, 1969, 1990). Typical perovskite materials of technological interests are piezoelectric Pb(Zr,Ti)O3, electrostrictive Pb(Mg,Nb)O3, and magnetoresistance (La,Ca)MnO3. There is much interest in exploiting the mystery of the perovskite structure and its family for understanding the functionality of materials, such as superconductivity, ferromagnetism, ferroelectricity, magnetoresistance, ionic conductivity, and dielectricity. Therefore, understanding perovskite and related structures is essential for research in functional materials because it could lead to discovering new materials with superior properties and unique functionality.