Corning developed a new ultra-slim flexible glass that can be used as a barrier film for flexible OLED displays. Corning claims that this new glass has the same barrier performance (for oxygen and moisture) as normal rigid glass. The whole thing is just 100 microns thick (0.1mm) and can withstand heat up to 400 degrees.
Corning is still developing the manufacturing process of this material, we do not know when it will be commercialized. A while back Corning published a nice video (a day made of glass) showing what's possible with flexible glass.
Just a few days ago, AGC unveiled their own thin flexible glass, which is also 0.1mm thick.