The book develops a comprehensive understanding of the surface impedance of the oxide high-temperature superconductors in comparison with the conventional superconductor Nb3Sn. Linear and nonlinear microwave responses are treated separately, both in terms of models, theories or numerical approaches and in terms of experimental results. The theoretical treatment connects fundamental aspects of superconductivity to the specific high-frequency properties. The experimental data review the state of the art, as reported by many international groups. The book describes further the main features of appropriate preparation, handling, mounting, and refrigeration techniques, and finally discusses possible applications in passive and active microwave devices.