An electronic device may have a support structure that supports a display and lenses. Each lens may be a reflective lens such as a catadioptric lens that receives polarized image light from the display and provides a corresponding image to an eye box. The display may be an emissive display with pixels that include light-emitting diodes. The light-emitting diodes may be overlapped by a light recycling layer such as a reflective polarizer or cholesteric liquid crystal layer. The light recycling layer recycles emitted light to enhance display efficiency.