This monograph presents a review of possible ways to reduce losses in waveguides and resonators, the formulation of boundary value problems of electromagnetics for cases when losses are considered, analytical and numerical methods of analysis. Chapter 1 deals with the formulation of impedance boundary conditions for the case of high skin effect in various conducting media. Chapter 2 presents the theory of regular waveguides with finitely conducting walls. Chapter 3 deals with the theory of cavities with absorbing surface and the medium inside. These chapters present the derivation of general formulae for the attenuation constant and Q-factor and consider concrete practical applications. There are also discussed principal errors associated with the solution of these problems. Chapters 4 and 5 deal with wave diffraction by imperfectly conducting gratings, both in free space and inhomogeneous anisotropic media. The main emphasis is laid on the description of dissipative resonance effects, in particular the effect of the abnormally low dissipation. Chapter 6 considers the attenuation of eigenmodes in periodic waveguides. It presents results obtained for low-loss flexible corrugated waveguides and high-quality corrugated resonators of the millimetre-wave band. A number of theoretical results confirmed by experiment are included in this book.