Nokia is demoing a concept phone with flexible display at Nokia World 2011 in London. The Nokia Kinetic by Nokia Research division works by bending and twisting the device in each corner in order to register input.
The Nokia Kinetic is a landscape device with two working applications, Music and Pictures, no doubt created as proof of concepts. For example bending in the device towards you will open the application.
Below is a video demo of the Nokia Kinetic and how it works. There are currently no plans to bring this screen technology to the market but this is merely a sneak into what Nokia has in store for us.