**Abstract**

So far, many microwave dielectric materials have been investigated for a range of telecommunication applications. In dielectrics, the three main dielectric properties are quality factor (*Q*), dielectric constant and temperature coefficient of resonant frequency. Among these, the most essential dielectric property is *Q*. More specifically, *Q* is the inverse of the dielectric loss (tan*δ*); thus *Q* = 1/tan*δ*. There are two kinds of losses: those depending on crystal structure and losses due to external factors. The former is intrinsic losses such as ordering, symmetry, and phonon vibration. The latter is extrinsic losses due to factors such as grain size, defects, inclusions and distortion. In this chapter, the authors present the origin of dielectric losses based on the crystal structure. An ideal and well-proportional crystal structure constitutes a low loss material. Most dielectric materials are paraelectrics with inversion symmetry *i* and high symmetry. In general, it is believed that ordering gives rise to a high *Q*, on which many researchers are casting doubt. In the case of complex perovskites, the symmetry changes from cubic to trigonal. Ordering and symmetry should be compared with the structure. In this chapter, three essential conditions for the origin of high *Q* such as high symmetry, compositional ordering and compositional density are presented.

**Keywords:** microwave dielectrics, *Q*-factor, ordering, symmetry, indialite/cordierite, pseudo tungsten-bronze, complex perovskite
