Nippon Electric Glass (NEG) developed the world's thinnest glass plate (only 30 um thick). The G-Leaf glass can be used as a substrate for flexible OLED displays, and NEG demonstrated a flexible OLED that is only 90 um thick (sandwiched between two G-Leaf sheets).
NEG uses their "overflow method" technology to manufacture the new glass plates. Reportedly the glass feels like a plastic film and does not break even when crumpled (see photo below).
Corning also has a flexible thin OLED glass product, called Willow Glass. Corning unveiled the Willow Glass line in 2012 - showing 50 um thick and 100 um variants.
In 2013, Nanomarkets analysed the opportunities for flexible glass and they see the market growing to over $2 billion before 2020. The OLED market is expected to adopt flexible glass for both displays and lighting panels.