This book focuses on the application of classical combustion theory to ignition and flame propagation in solid-solid and gas-solid systems. It presents experimental investigations in the areas of local ignition, filtration combustion, self-propagating high temperature synthesis and nanopowders protection. The authors highlight analytical formulas used in different areas of combustion in solids and propose an approach based on classical combustion theory. The book attempts to analyze the basic approaches to understanding of solid-solid and solid - gas combustion presented in contemporary literature in a unified approach based on classical combustion theory.