I have seen in a number of research labs around the world over the past few years several concept phones that had a curved space and a few that had some sort of flexibility. So far it looked to me as the demonstration of what OLED and a bit of flexible electronics could do: extending the possibility of designer to create fancier products.
So far no product has been released (unless you count phones like the LG GFlex phone that has been designed with a curved surface but whose flexibility is really limited) and probably this will be so for a few more years. One of the problem is that the flexibility of the screen, that is technologically feasible with OLED screens, is not matched by the flexibility of the battery, still a crucial component in any cell phone, nor by the flexibility of chips. Flexible electronics is a reality but does not deliver the kind of processing capacity we've got used to in a phone and that is today a must to run many of the applications we have come to expect as standard features.
So, in a way, this news coming from Queen's University should not be seen as a game changer. At the Queen's Human Media Lab researchers have used "bendable" technology to prototype a cell phone, ReFlex, and created a human machine interface that exploits this "bendability". To make it work the researchers created a phone with two "handles" that embed the non flexible batteries and the chips to control the screen connected by the bendable screen with stretch sensors on the back.
As an example, look at the video clip for more, they have decided that as you are reading an eBook on the phone the turning of the page can be activated by a slight bending of the phone with your hand, similarly to what you would do with a paperback.
Apple has shown several times how to use innovative technology to reshape the HMI creating a compelling user experience. Indeed this is what has the most impact on us, the users.
Seeing researchers studying how to best exploit flexible electronics is good, although we will have to wait for flexible batteries and this is not in sight, yet.