The crystal chemistry of complex perovskite dielectric oxides is reviewed, with an emphasis on structures derived from ordering of the cations on the octahedral B-sites. New classes of perovskites, designed to exhibit 1:2 or 1:3 B-site order for application as low-dielectric-loss microwave ceramics, are identified, and their synthesis, structure, and properties are described. Through the use of B-site chemistries based on Li, Nb, Ta, Ti, and W, members of four new families with 1:2 order, A(β1/3Iβ 2/3II)O3, and three new families with 1:3 order, A(β1/4Iβ3/4 II)O3, were successfully prepared. The formation and stability of the new and previously prepared ordered perovskites are rationalized through the use of familiar crystal chemical tools such as cation size and charge difference, bond valence, tolerance factor, and new concepts related to the local charge imbalance on the A- and B-sublattices. These tools can be successfully applied to develop stability field maps for each structure and to predict other new ordered systems.