An electronic device may have a display. Inactive portions of the display such as peripheral portions of the display may be masked using an opaque masking layer. An opening may be provided in the opaque masking layer to allow light to pass. For example, a logo may be viewed through an opening in the opaque masking layer and a camera may receive light through an opening in the opaque masking layer. The display may include upper and lower polarizers, a color filter layer, and a thin-film transistor layer. The opaque masking layer may be formed on the upper polarizer, may be interposed between the upper polarizer and the color filter layer, or may be interposed between the color filter layer and the thin-film transistor layer. The upper polarizer may have unpolarized windows for cameras, logos, or other internal structures.