LG sees a bright future for flexible displays. In fact the company predicts that flexible smartphones will take-up 40% of the smartphone market in 2018. Samsung thinks the same, and they are basing their numbers on DisplaySearch - which means that LG is also probably actually quoting the same source.
LG Electronic's mobile product planning chief, Dr Ramchan Woo, says that "we are bored of flat" and that a flexible device is much more than just a flexible display. For example one of the key technologies in the G Flex is the flexible Stack & Folding battery made by LG Chem (here's a photo of the battery). Another key technology is the thin cover glass - and so we learn that this phone, similarly to Samsung's Galaxy Round also includes a cover glass, which explains why it is not truly "unbreakable".
Dr Woo though says that LG tested the G Flex with a pressure of 40 Kg, and unofficially it survived much more (it deforms to be flat and then springs back to its regular shape). You can do this a hundred times without any damage to the construction. LG says that truly bendable and flexible devices will come in the future - but it will take around a decade before such devices will hit the market.