An electronic device is provided with a display such as a liquid crystal display. The display includes a liquid crystal display module an array of display pixels. A backlight unit is used to provide backlight illumination to the display module. A shutter module having local dimming elements is used to locally control the amount of light that is transmitted through the display. The local dimming elements can be formed from liquid crystal display structures, polymer-dispersed liquid crystal display structures, photovoltaic material, electrowetting display structures, and/or other suitable light controlling elements. Each local dimming element controls the amount of light that is transmitted through an overlapping region of the array of display pixels. The local dimming elements may be arranged in a uniform array having rows and columns or may be shaped and sized differently and located in specific regions of the display.
