Tactile perception is an important modality for dexterous manipulation, but faces unique challenges in that the sensor has to wrap around the system. Biological skin solves these problems extremely well. Not only can it detect contacts, but it also grows on complex three-dimensional shapes, stretches with underlying soft tissue and around joints, and leaves enough space inside for other organs. Previous artificial sensors could only achieve different subsets of these features. We present a novel tactile sensor skin which is completely made from elastic silicone rubber and can stretch to multiple times its original length without damage. It can be produced in three-dimensional double-curved shapes, is thin enough to accommodate other robot components or human body parts, and it can measure forces and locations of multiple simultaneous contacts. We develop production methods and material formulations, algorithms for computer-aided design, compact readout electronics using small, low-power FPGAs, firmware, and software.INDEX TERMS Tactile sensors, robot sensing systems, robot learning, soft robotics.