In this chapter, the authors explain electromagnetic waves in waveguides and oscillations in resonators containing gyrotropic media, in particular, the magnetized ferrites. The treatment in terms of coupled waves is especially useful if the distinction between the waves in the waveguide with a gyrotropic medium and the corresponding waves in the waveguide with an isotropic medium is small. In the case of a microstrip or a coaxial waveguide, a dielectric sample should be inserted to obtain such points. Microstrip and coaxial waveguides with dielectric and ferrite samples cannot be analyzed rigorously, and a parallel-plane waveguide is often used as an approximate model. Resonators with small ferromagnetic, ferrimagnetic, or antiferromagnetic samples, mostly spheres, are widely used in measurements of the magnetic-resonance parameters: the resonance field and the resonance linewidth. The nonreciprocity, which appears when the ferrite sample is located at a point of the circular polarization of the magnetic field, provides a possibility to realize a filter-circulator.