A display may have an array of display pixels that generate an image. A coherent fiber bundle may be mounted on the display pixels. The coherent fiber bundle may have a first surface that is adjacent to the display pixels and a second surface that is visible to a viewer. The coherent fiber bundle may contain fibers that carry light from the first surface to the second surface. The second surface may be planar or may have a central planar region and curved edge regions that run along opposing sides of the central planar region. The fibers may have cross-sectional surface areas with a first aspect ratio on the first surface and a second aspect ratio that is greater than the first aspect ratio on the second surface.