All commercial forms of electronic/optoelectronic technologies use planar, rigid substrates. Device possibilities that exploit bio-inspired designs or require intimate integration with the human body demand curvilinear shapes and/or elastic responses to large strain deformations. This article reviews progress in research designed to accomplish these outcomes with established, high-performance inorganic electronic materials and modest modifications to conventional, planar processing techniques. We outline the most well developed strategies and illustrate their use in demonstrator devices that exploit unique combinations of shape, mechanical properties and electronic performance. We conclude with an outlook on the challenges and opportunities for this emerging area of materials science and engineering.