The science of biomimetics seeks to gain inspiration from nature for the development of new engineering solutions. This article reviews some of the work done to understand fatigue-resistant structures in nature. Evolution has created materials and components which are highly resistant to cyclic loading, using a number of interesting strategies: (i) careful control of geometry to minimise stress concentration; (ii) sophisticated use of fibre composites taking advantage of anisotropy, fibre insertions at joints and functional grading, to create structures with no weak interfaces; (iii) hollow, tubular components with optimised fatigue strength taking account of all possible failure modes, and; (iv) continuous monitoring and repair of fatigue cracks in service. In each case an attempt has been made to quantify the potential improvement and to outline the possibilities for future transport applications.