A display may have an active area surrounded by an inactive border area. The inactive border area may be provided with an opaque masking material. The display may be a liquid crystal display having a liquid crystal layer sandwiched between a color filter layer and a thin-film transistor layer. Upper and lower polarizers may be provided above and below the color filter and thin-film transistor layers. The upper polarizer may have a polarized central region that overlaps the active area of the display. The upper polarizer may also have an unpolarized portion in the inactive border area overlapping the opaque masking material. The opaque masking material may alternatively be formed on the underside of a clear polymer substrate that is attached to the display above the upper polarizer or may be incorporated within the layers that make up the upper polarizer.