We consider the main achievements and problems in the field of proton-conducting solid electrolytes. Because of the extremely small proton radius, mechanisms of proton transport differ drastically from those for other ions. This review examines general aspects of proton transport in low- and intermediate-temperature proton-conducting solid electrolytes, such as hydrated acids, acid salts, and bases and anhydrous acid salts. Proton transport in these materials is due to a sequence of rotations of proton-containing groups and proton hops between them.