An electronic device may have a display. The display has pixels configured to display an image. The display is mounted in a housing. The housing may include head-mounted support structures configured to support the display for viewing through lenses. The pixels of the display may be covered by a layer of thin-film encapsulation. The thin-film encapsulation may be covered with a cover layer such as a glass cover layer that is attached to the thin-film encapsulation layer by a layer of adhesive. To suppress internal light reflections, the display may include reflection suppression structures. The reflection suppression structures may include an antireflection layer and/or polarizer and waveplate layers. The reflection suppression structures may be formed on an outwardly facing surface of the cover layer and/or between the thin-film encapsulation layer and the cover layer.