Flexible displays based on various forms of organic LEDs (or OLEDs) will allow us to carry roll-up TVs one day. Or you'll deploy a screen embedded in a pen to talk with your friends. But there are still significant hurdles, according to Electronics Weekly in "Organic LEDs are on the way."
One major obstacle is the life expectancy for such screens, still far below from the 10,000 hours limit considered to be the basis for a commercial distribution. But there is a bigger issue. On OLEDs displays, the different colors vanish at different rates. So you'll lose blue three times before red or green.
Another very long and well-documented article on displays from Military & Aerospace Electronics, "Display technology leaps to the next generation," adds that there is still a massive $1 billion per year poured in OLED research, and that 14-inch OLED displays are already working in labs.
This overview contains selected excerpts of the two articles mentioned above.