Insertion is a widely utilized process for reversibly changing the stoichiometry of a solid through a chemical or electrochemical stimulus. Insertion is instrumental to many energy technologies, including batteries, fuel cells, and hydrogen storage, and has been the subject of extensive investigations. More recently, solid-state switching devices utilizing insertion have drawn significant interest; such devices dynamically switch a material's chemical stoichiometry, changing it from one state to another. This review illustrates the fundamental properties and mechanisms of insertion, including reaction, diffusion, and phase transformation, and discusses recent developments in characterization in these fields. We also review new classes of recently demonstrated insertion devices, which reversibly switch mechanical and electronic properties, and show how the fundamental mechanisms of insertion can be used to design improved switching devices.