Electronic devices may be provided with displays having polarizer structures. Polarizer structures may incorporate flexible layers of glass. The flexible glass layers may be laminated to other sheets of material in the polarizer structures using roll-to-roll lamination equipment. After the polarizer structures are cut into panels, the panels may be laminated to liquid crystal display structures, organic light-emitting-diode display structures or other display structures using sheet-to-sheet lamination tools. Ultraviolet-light-blocking material may be incorporated into a display to prevent damage to the polarizer layers in the polarizer structures. Coatings such as antireflection coatings, antistatic coating, and anti-smudge coatings may be provided on the polarizer structures. Displays may use the flexible glass layers and additional protective layers to prevent a polarizer layer from being exposed to excessive moisture. A birefringent layer may be incorporated into a display and may serve as a protective layer for a polarizer.