In the critical area of sustainable energy storage, solid-state batteries have attracted considerable attention due to their potential safety, energy-density and cycle-life benefits. This Review describes recent progress in the fundamental understanding of inorganic solid electrolytes, which lie at the heart of the solid-state battery concept, by addressing key issues in the areas of multiscale ion transport, electrochemical and mechanical properties, and current processing routes. The main electrolyte-related challenges for practical solid-state devices include utilization of metal anodes, stabilization of interfaces and the maintenance of physical contact, the solutions to which hinge on gaining greater knowledge of the underlying properties of solid electrolyte materials.