Despite being first demonstrated over 160 years ago, and offering significant environmental benefits and high electrical efficiency, it is only in the last two decades that fuel cells have offered a realistic prospect of being commercially viable. The solid oxide fuel cell (SOFC) offers great promise and is presently the subject of intense research activity. Unlike other fuel cells the SOFC is a solid-state device which operates at elevated temperatures. This review discusses the particular issues facing the development of a high temperature solid-state fuel cell and the inorganic materials currently used and under investigation for such cells, together with the problems associated with operating SOFCs on practical hydrocarbon fuels.