The chapter is devoted to the study of the electromagnetic wave propagation in cylindrical waveguides of circular cross section. A homogeneous dielectric waveguide of circular cross section, a dielectric rod (DR), and a perfectly conducting cylinder covered with a homogeneous dielectric material layer, the Goubau line (GL), are taken as model waveguides. The following types of dielectric materials are considered: inhomogeneous dielectric, metamaterial, anisotropic dielectric, absorption dielectric, and chiral medium.