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 a sheet of glass or another optical member may have portions that are configured to bend light from the display pixels along the periphery of the active display structure. The optical member may have an area that is larger than the area of the active display structure, so that the presence of the optical member may serve to enlarge the apparent size of the display. Solidified liquid polymer may be used to support the optical structures and may be interposed between the optical structures and the active display structures.