Yoon Bu-hyun, LG Electronics's mobile business VP said that LG plans to launch a mobile phone that has an unbreakable flexible OLED display in Q4 2013. LG Display started working on these flexible OLEDs in late 2011 and they consider those displays to have a real value for the mobile solution (as opposed to glass based OLEDs which LG considers inferior to LCDs for mobile applications).
The last time we heard from LG Display regarding their flexible OLED was in January 2013. Back then the company said it was on track to start mass production of plastic based flexible OLEDs in H2 2013. The capacity will be "very limited" and they expect to be able to support just one or two customers. LG Display's flexible OLEDs will use polyimide coated substrate and direct-emission RGB sub-pixels (as opposed to LG's OLED TV which use white OLEDs with color filters).
Just a few days ago we reported that the OLED Association says that Samsung's upcoming Galaxy Note 3 will use a YOUM display (a plastic-based unbreakable flexible OLED). I'm guessing LG does not want to be left behind, so it may be that they will launch a very low-volume phone just so they won't be perceived as being less technology advanced than Samsung on flexible OLEDs.
LG Display is also working on curved OLED TVs. In January LG has unveiled a 55" curved OLED TV, called the EA9800, and some company official claims that the company aims to launch these TVs in the second half of 2013.
Another LG company, LG Chem, is on track to release the world's first flexible OLED lighting panels in July 2013. Seems that LG is set to become the leader in flexible OLEDs - for both displays and lighting applications.