An LCD works by selectively blocking light from a backlighting unit (BLU, usually made from LEDs) using a crystal which changes its polarization-filtering when voltage is applied. An electrochromic device is similar in idea but more simple as they can be turned from being transparent to being opaque. These kind of displays haven't been commercialized successfully yet due to fragile materials and material mismatches with the electrodes.
But new research at Bilkent University shows that graphene can be used to create such a device that features high percentage optical modulation, optical tuning properties in the UV to infrared, good electrical conductivity with no material mismatches. The display is mechanically flexible.
It's not clear if this material is suitable for actual displays, but it may be possible to use it for applications such as smart windows or reconfigurable mirrors.