An electronic device may be provided with a display. The display may include a liquid crystal display cell and an organic light-emitting diode backlight unit. The liquid crystal display cell may include a color filter layer, a liquid crystal layer, and a thin-film transistor layer. The organic light-emitting diode backlight unit may include organic emissive material formed on a substrate. The organic emissive material may generate backlight for liquid crystal display cell. Display pixels in the liquid crystal display cell may control the emission of the backlight from the display. The organic light-emitting diode backlight unit may be attached to the display using adhesive, laminated to a polarizer layer of the display cell, or may be integrated into the liquid crystal display cell. The backlight unit may include conductive vias or bent extended edge portions for coupling the backlight unit to control circuitry.