This review aims to assess publications relevant to understanding the rate-dependent dynamic behaviour of glass- and carbon-fibre reinforced polymer composites (FRPs). FRPs are complex structures composed of fibres embedded in a polymer matrix, making them highly anisotropic. Their properties depend on their constituent materials as well as micro-, meso- and macro-scale structure. Deformation proceeds via a variety of damage mechanisms which degrade them, and failure can occur by one or more different processes. The damage and failure mechanisms may exhibit complex and unpredictable rate-dependence, with certain phenomena only observable under specific loading conditions or geometries. This review focusses on experimental methods for measuring the rate-dependent deformation of fibre composites: it considers high-stain-rate testing of both specimens of ‘simple’ geometry as well as more complex loadings such as joints, ballistic impact and underwater blast. The effects of strain rate on damage and energy-based processes are also considered, and several scenarios identified where strength and toughness may substantially decrease with an increase in strain rate.