An electronic device may have control circuitry coupled to input-output devices such as a display. A flexible input-output device may be formed from an elastomeric substrate layer. The substrate layer may have signal paths to which components are mounted. Openings may be formed in the elastomeric substrate layer between the signal paths to create a stretchable mesh-shaped substrate. The electrical components may each include an interposer having solder pads soldered to the elastomeric substrate. Electrical devices such as micro-light-emitting diodes may be soldered to the interposers. The electrical components may also include electrical devices such as sensors and actuators. A stretchable lighting unit may have a stretchable light guide illuminated by a stretchable light source.