Abstract This chapter reviews ceramic-matrix composites with potential for high-temperature engineering applications. The main reinforcing fibres are silicon carbide, and these have been used in a number of matrices from glass, glass ceramic, silicon nitride and silicon carbide (with increasing refractoriness). Comment is made about choice of systems, background theory, test methods and experimental data. For one-dimensional reinforcement, there is good agreement between experiment and theory. Key future requirements include: fibres with increased refractoriness; fabrication methods for components with two- and three-dimensional reinforcement and of complex shape; better understanding of a range of mechanical properties and definition of engineering requirements.