A display may have an array of pixels formed from organic light-emitting diodes and thin-film transistor circuitry. The organic light-emitting diodes may be interposed between a substrate (30) and a cover layer (70). The organic light-emitting diodes may be white light-emitting diodes (26) that emit white light that is filtered through a color filter array (76) to produce colored light. The color filter array may be located above or below the array of light-emitting diodes. A microcavity may be formed between the substrate (30) and each light-emitting diode (26). The microcavity may be formed from an anode (36) in the light-emitting diode and first (86) and second layers (78) with different refractive indices. The low-refractive-index layer may be formed from a color filter in the color filter array. Light from the light-emitting diode may resonate within the microcavity beneath each light-emitting diode before exiting the display as colored light.