<p>A review of the current state and prospects for the study of compositionally complex oxide (CCO) materials containing high-entropy oxides (HEO) and medium-entropy mixed oxides (MEMO) as dielectrics for microwave applications is presented. Fundamental approaches to the formation of stable solid solutions are considered, in particular, selection criteria for the structural type (perovskite, spinel, and garnet), cationic composition, as well as thermodynamic formation conditions. Experimental data on CCO dielectric properties in different dielectric constant ranges (ε) compared to traditional microwave dielectrics are analyzed. It is shown that CCO systems exhibit a unique combination of phase stability, controllable parameters ε, <i>Qf</i>, and frequency temperature stability τ_<i>f</i>, and also have the potential for development of next-generation microwave components. Considerable attention is paid to methods for predicting stability and dielectric properties, such as thermodynamic, quantum-chemical, and methods with elements of machine learning.</p>