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Biology relies on classes of materials that are soft and elastic, in structures that have complex curvilinear geometries. By contrast, all known high performance electronic/optoelectronic systems are built on the rigid, brittle planar surfaces of semiconductor wafers. Technologies that bridge this gap in form and mechanics create new opportunities in devices that adopt biologically inspired designs or require intimate integration with the human body. This paper reviews concepts for building electronics that combine hard and soft materials in ways that can exploit established semiconductors such as silicon, gallium arsenide, gallium nitride in systems that have the mechanical properties of a rubber band. Due to the central role of mechanics and physical motions in these systems, they can be considered also as a type of MEMS technology. Application examples include (1) bio-integrated systems capable of monitoring and delivering various forms of therapy, and (2) bio-inspired, `eyeball' cameras for wide field-of-view imaging.