The content of the review covers, first, generalities on creep. Then, the creep of ceramics and fibres, that are key constituents of fibre-reinforced ceramic matrix composites (CMCs) are addressed. The general features of ceramic matrix composites that may influence the creep behaviour and creep rupture are discussed. Emphasis is placed on microstructure-property relationships and load sharing between fibres and matrix that are critical for CMCs. Then, creep tests and the creep behaviour of various types of fibre-reinforced composites are presented. Mechanisms and models are discussed. The influence of various factors including composite structure, constituent properties (matrix and fibres), interfacial properties and environmental conditions are examined. The paper focuses on non-oxide composites like SiC/SiC that received much attention during the last three decades. Creep of oxide ceramics, fibres and composites are addressed more briefly.