Those few devices with curved displays currently on the market use flexible OLED screens, but this might change soon. Since this approach ends up with quite expensive displays, Japan Display has introduced a 5.5-inch flexible screen that uses the older, but also cheaper, LCD technology.
According to the official press release, the technology used for this screen is known as Full Active Flex and "uses a plastic substrate for both sides of the liquid crystal layer." Thanks to its ability to support a refresh rate as low as 15 Hz, this display allows for a significant drop in power consumption.
The 5.5-inch display that uses Full Active Flex has a typical contrast ratio of 1,500:1 and 500 cd brightness. It has a full HD resolution and offers a density of 401 ppi, so it definitely will not be used for high-end devices. Sadly, mass production is not expected to start before the end of the year.