This monograph offers a comprehensive overview of the current state of research utilizing quantum chemistry methods to explore the electronic structure, chemical bonding, and physicochemical properties of carbides and nitrides of d- and f-block elements. It analyzes the computational methods used to calculate the spectroscopic, electrical, magnetic, superconducting, and thermomechanical properties of these compounds. The results of the investigation into the electronic energy structure of complex double carbide and nitride phases of transition metals are presented in detail, along with the influence of structural vacancies on their electronic and physicochemical characteristics across a wide concentration range. The book also summarizes findings on the peculiarities of energy states, chemical bonding, and the properties of multicomponent alloys based on high-temperature carbide and nitride phases. Additionally, it organizes material related to the study of the electronic structure of the surfaces of refractory compounds. This book is intended for specialists in the fields of solid-state physics and chemistry, physical chemistry, and materials science, as well as for graduate students and advanced undergraduates in related disciplines.