IHS estimates that the flexible display market will grow very fast, with a CAGR of 44% from 2014 onwards - to reach a market of $23 billion in 2024 (as flexible displays, mostly OLEDs, will grab 15% of the total flat panel display market).
Today IHS says that they see foldable display (in tablets and smartphones) appearing as early as next year. IHS sees 180 million foldable displays sold in 2020, which means foldable displays will take up 51% of the total flexible display market.
We've seen foldable displays demonstrated by several companies, including Samsung, Nokia/SEL and ITRI. Samsung seems to be quite close to actual foldable-display commercialization and demonstrated two foldable OLED prototypes towards the end of 2014 - a 5.5" (WQXGA, 2048x1526, 464 PPI) panel that folds in half and a 10" tri-foldable AMOLED (Full-HD, 218 PPI). Samsung's original plan was to release a foldable phone in 2015, but we'll be very pleased to see one on the market in early 2016 as IHS forecasts!