Inorganic light-emitting diodes and photodetectors represent important, established technologies for solid-state lighting, digital imaging and many other applications. Eliminating mechanical and geometrical design constraints imposed by the supporting semiconductor wafers can enable alternative uses in areas such as biomedicine and robotics. Here we describe systems that consist of arrays of interconnected, ultrathin inorganic light-emitting diodes and photodetectors configured in mechanically optimized layouts on unusual substrates. Light-emitting sutures, implantable sheets and illuminated plasmonic crystals that are compatible with complete immersion in biofluids illustrate the suitability of these technologies for use in biomedicine. Waterproof optical-proximity-sensor tapes capable of conformal integration on curved surfaces of gloves and thin, refractive-index monitors wrapped on tubing for intravenous delivery systems demonstrate possibilities in robotics and clinical medicine. These and related systems may create important, unconventional opportunities for optoelectronic devices.