An electronic device may have a display such as a liquid crystal display. The display may have multiple display layers for generating display light such as a color filter layer and a thin-film transistor layer. The display may include first and second layers of optical fibers formed over the display layers. The first and second layers of optical fibers may guide display light generated in the display layers to an outer surface of the display. The first layer of optical fibers may include optical fibers having a first numerical aperture. The second layer of optical fibers may include optical fibers having a second numerical aperture. The first numerical aperture may be smaller than the second numerical aperture. The second layer of optical fibers may include vertical and angled optical fibers. The angled optical fibers may help reduce the size of an inactive region around the center of the display.