Publisher Summary The aim of most modern research into fast-ion conductors is to produce materials that show highly conductive behavior at relatively low temperatures for convenient incorporation into electrochemical devices. One new and important concept which has emerged, involving fast-ion conductivity, is the insertion compound or solid-solution electrode. In a solid-solution electrode there is both rapid ion transport and electronic conductivity, but a third vital ingredient is the presence of a range of stoichiometry involving the mobile ion. Fast-ion conducting materials of this type, therefore, can be used not as electrolytes, as is the case for β-alumina, but a battery electrode with either a liquid electrolyte or a solid electrolyte. In the latter case fast-ion conducting materials are used to make an all-solid-state battery. In the former case, although the arrangement of solid and liquid phases is formally similar to that found in conventional lead-acid or alkaline batteries, the energy densities obtainable using modern materials are much higher than previously thought possible.