This book is dedicated to various aspects of electromagnetic wave theory and its applications in science  and technology. The covered topics include the fundamental physics of electromagnetic waves, theory of electromagnetic wave propagation and scattering, methods of computational analysis, material  characterization, electromagnetic properties of plasma, analysis and applications of periodic structures and waveguide components, and finally, the biological effects and medical applications of electromagnetic fields. Even though the classical electromagnetic theory is well-established and experimentally verified, it is far from being a closed subject. In spite of the fact that the theory is capable of providing explanations for all (classical) electromagnetic effects, there are several fundamental problems that remain open. These problems mainly concern the electromagnetic waves behaving like quantum particles. In order to complete the theory of electromagnetic waves, a new fundamental physics emerged suggesting novel concepts to explain observed physical phenomena. The first part of this book is dedicated to the research in this field including various aspects of vacuum field theory, electromagnetic wave contribution to the quantum structure of matter, and matter waves. Modelling and computations in electromagnetics is a fast-growing research area. The general interest in this field is driven by the increased demand for analysis and design of non-canonical electromagnetic structures and rapid increase in computational power for calculation of complex electromagnetic problems. The second part of this book is devoted to the advances in the analysis techniques such as the method of exact absorbing boundary conditions, fractional operator approach, and fractional boundary conditions. The problems of diffraction on infinitely thin surfaces are considered, and the difficulties in the analysis of axially-symmetrical open resonators are addressed. The third part of the book deals with electromagnetic wave propagation and scattering effects. The main focus is made on atmospheric refraction and propagation in the lower troposphere, atmospheric attenuation due to the humidity, interaction of electromagnetic waves with inhomogeneous media composed of complex particles, modelling of scattering from random rough surfaces, and the problems of propagation in waveguides with mperfectly reflecting boundaries Waveguides are essential parts of millimetre and submillimetre-wave devices and systems. They are used for guiding electromagnetic energy between the components of the system. In the mentioned frequency band, periodic structures are also often used for wave guiding as well as for realization of delay lines, filter elements, and interaction structures in vacuum electron devices. The fourth part of the book starts with the description of the method of matrix formalism and its application to the analysis of planar waveguides and periodic structures. Then, the open resonators and open waveguides employing periodic structures and their implementation in vacuum electron devices are considered. The fourth part concludes with a chapter on waveguide mode converters. The fifth part of the book is dedicated to interaction of electromagnetic waves with materials and implementation of electromagnetic methods for material analysis and characterisation. This includes scattering and generation of waves on cubically polarisable dielectrics, electromagnetic properties of elastomers, temperature behaviour of microwave absorption in ferrites and permittivity of soil. Time and frequency domain measurement  techniques are also considered here. Plasma technology is becoming increasingly attractive for radio communications, radio astronomy and military (stealth) applications due to electromagnetic properties of plasma medium. The shielding properties of plasma are investigated in the sixth part of this book. The final (seventh) part of this book deals with biological effects of electromagnetic radiation and its  implementation to medical imaging, particularly, sensitivity and resolution improvement of molecular imaging using magnetic nanoparticles. The presented material in this book is based on recent research work conducted by the authors working within the covered topics, who deserve all the credits for the presented scientific results.