The ability of fibre reinforced composites to deform with a non-linear stress–strain response and gradual, rather than sudden, catastrophic failure is reviewed. The principal mechanisms by which this behaviour can be achieved are discussed, including ductile fibres, progressive fibre fracture and fragmentation, fibre reorientation, and slip between discontinuous elements. It is shown that all these mechanisms allow additional strain to be achieved, enabling a yield-like behaviour to be generated. In some cases, the response is ductile and in others pseudo-ductile. Mechanisms can also be combined, and composites which give significant pseudo-ductile strain can be produced. Notch sensitivity is reduced, and there is the prospect of increasing design strains whilst also improving damage tolerance. The change in stiffness or visual indications of damage can be exploited to give warning that strain limits have been exceeded. Load carrying capacity is still maintained, allowing continued operation until repairs can be made. Areas for further work are identified which can contribute to creating structures made from high performance ductile or pseudo-ductile composites that fail gradually.