An electronic device may include a display. The display may be formed by an array of light-emitting diodes mounted to the surface of a substrate. The substrate may be a silicon substrate. Circuitry may be located in spaces between the light-emitting diodes. Circuitry may also be located on the rear surface of the silicon substrate and may be coupled to the array of light-emitting diodes using through-silicon vias. The circuitry may include integrated circuits and other components that are attached to the substrate and may include transistors and other circuitry formed within the silicon substrate. Touch sensor electrodes, light sensors, and other components may be located in the spaces between the light-emitting diodes. The substrate may be formed from a transparent material that allows image light to reach a lens and image sensor mounted below the substrate.