An electronic device may be provided with a display mounted in a housing. The display may have an array of display pixels that provide image light to a user. The array of display pixels may form an active display structure with a rectangular shape. The rectangular active display structure may be surrounded by an inactive border region. Optical structures such as upper structures formed from a sheet of glass and lower optical structures that lie beneath the sheet of glass may be configured to bend light from the display pixels along the periphery of the active display structure. The upper optical structures may have an area that is larger than the area of the active display structure, so that the presence of the optical structures may serve to enlarge the apparent size of the display. The lower and upper optical structures may have curved surfaces for bending the light.