The importance of biological materials has long been recognized from the molecular level to higher levels of organization. Whereas, in traditional engineering, hardness and stiffness are considered desirable properties in a material, biology makes considerable and advantageous use of softer, more pliable resources. The development, structure and mechanics of these materials are well documented and will not be covered here. The purpose of this paper is, however, to demonstrate the importance of such materials and, in particular, the functional structures they form. Using only a few simple building blocks, nature is able to develop a plethora of diverse materials, each with a very different set of mechanical properties and from which a seemingly impossibly large number of assorted structures are formed. There is little doubt that this is made possible by the fact that the majority of biological 'materials' or 'structures' are based on fibres and that these fibres provide opportunities for functional hierarchies. We show how these structures have inspired a new generation of innovative technologies in the science and engineering community. Particular attention is given to the use of insects as models for biomimetically inspired innovations.