Most electroceramics are ferroelectrics, but microwave dielectrics are mostly paraelectrics with a center of symmetry i. Microwave dielectrics should possess a perfect crystal structure with neither defects nor internal strain in order to be microwave friendly. They have been used in resonators and filters in mobile telecommunications devices. Perovskite and related compounds are also mostly ferroelectrics, but paraelectrics with a perovskite structure also exist, and are used in microwave dielectrics. Owing to the flexibility of the perovskite structure, many kinds of microwave dielectrics with a perovskite structure have been designed for microwave dielectrics. In this chapter, simple and complex perovskite, and perovskite related materials such as pseudo-tungsten-bronze solid solutions and homologous compounds are introduced for microwave dielectrics. The microwave dielectric properties are revealed through the crystalline structure of the material. Therefore, the relationship between the crystalline structure and properties of the material is presented, and is expected to be of use in the design of novel dielectrics. As many superior materials for microwave dielectrics have been developed and are expected to be used in new applications such as wireless sensors and wireless power transfer by resonant coupling, wave absorption by interference and transparent ceramics with no birefringence, these new applications are also discussed.