Autonomic self-healing materials, where initiation of repair is integral to the material, are being developed for engineering applications. This bio-inspired concept offers the designer an ability to incorporate secondary functional materials capable of counteracting service degradation whilst still achieving the primary, usually structural, requirement. Most materials in nature are themselves self-healing composite materials. This paper reviews the various self-healing technologies currently being developed for fibre reinforced polymeric composite materials, most of which are bioinspired, inspired by observation of nature. The most recent self-healing work has attempted to mimic natural healing through the study of mammalian blood clotting and the design of vascular networks found in biological systems. A perspective on current and future self-healing approaches using this biomimetic technique is offered. The intention is to stimulate debate outside the engineering community and reinforce the importance of a multidisciplinary approach in this exciting field.