The use of ceramics in fusion power reactors is reviewed. Radiation effects can limit the useful lifetime of ceramic components by changing the dimensions, mechanical properties, thermal conductivity, and electrical properties. The brittleness and statistical spread in strength of monolithic ceramics causes problems for mechanical design which may be alleviated by the use of new ceramic/ceramic composites. Recently developed SiC fiber/SiC matrix composites have good mechanical properties which are likely to be retained after neutron irradiation.