LG Display posted an interesting article explaining their plastic-based flexible OLED technologies and displays - showing how these displays are better than LCD displays in several aspects (mainly the fact that plastic OLEDs are thinner than LCDs and glass-based OLEDs). In addition, LG Display posted their flexible OLED roadmap:
As you can see, LG already produces flexible OLEDs for phones and wearable devices. In 2015-2016 the company sees flexible OLEDs being adopted in tablets and bendable phones. From 2017, LGD sees flexible OLEDs being used to produce foldable and rollable devices.
LG also aims to produce rollable TVs in 2017. In July 2014, the company unveiled a 18" flexible OLED prototype panel. LG is still confident that it will be able to develop a 60" UHD flexible and transparent OLED by 2017.