Inorganic semiconductors such as silicon, gallium arsenide, and gallium nitride provide, by far, the most well-established routes to high performance electronics/optoelectronics. Although these materials are intrinsically rigid and brittle, when exploited in strategic geometrical designs guided by mechanics modeling, they can be combined with elastomeric supports to yield integrated devices that offer linear elastic responses to large strain (∼100%) deformations. The result is an electronics/optoelectronics technology that offers the performance of conventional wafer-based systems, but with the mechanics of a rubberband. This article summarizes the key enabling concepts in materials, mechanics, and assembly and illustrates them through representative applications, ranging from electronic “eyeball” cameras to advanced surgical devices and “epidermal” electronic monitoring systems.