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 light-emitting diodes may be inorganic light-emitting diodes formed from separate crystalline semiconductor structures. An array of pixel control circuits may be used to control light emission from the light-emitting diodes. Each pixel control circuit may be used to supply drive signals to a respective set of the light-emitting diodes. The pixel control circuits may each have a silicon integrated circuit that includes transistors such as emission enable transistors and drive transistors for supplying the drive signals and may each have thin-film semiconducting oxide transistors that are coupled to the integrated circuit and that serve as switching transistors.