According to an interesting market report from ETNews, LG Eelctronics is developing a smartphone with a bendable display. This technology will be similar to the bendable OLED TV prototypes we've seen, so you could press a button to change the phone from a curved state to a flat state. LGE has reportedly filed for a US patent describing such a system.
ETNews says that this phone will actually be released very soon, and will be called the G Flex 2. We heard reports before that the G Flex 2 will be launched next month at CES 2015. I'm a bit skeptical that this will be a bendbale phone, as it seems a bit too early for a bendbale phone, but I wouldn't mind a good surprise from LGE!
A couple of months ago I reported that LG Electronics is also developing a mini-version of the curved G Flex phone.
LG's G Flex, the first device to use LG Display's flexible plastic OLED display, has a 6" 720p flexible OLED display that is curved from top to bottom (unlike Samsung's Galaxy Round which is curved from left to right). The G Flex used a curved battery produced by LG Chem. In March 2014 I posted a review of the G Flex.