Seemingly out of nowhere, shape — not screen size or color — has emerged as the new battleground in the smartphone wars. In October, Samsung unveiled the first-ever “curved display” smartphone (the Galaxy Round) and in November, LG followed with another curved display phone that also happened to be flexible (the G Flex). And now come rumors that Apple is bringing two new curved iPhones to market  sometime late next year. It’s now all about shape, as companies begin to develop and deliver phones that are “curved,” “round,” “flexible,” and even “bended.”

The big question, though, is whether simply changing the shape of the phone actually leads to innovative new types of user experiences, or whether this is all a bit of marketing sleight-of-hand to get us to buy the next smartphone.

For now, there doesn’t seem to be anything terribly innovative in slightly changing the shape of a screen. It’s more a novelty. For example, the new curved display Samsung phone, the Galaxy Round, enables a nifty little “roll effect,” in which you can slightly rock the curved phone, so that you can retrieve basic information from the phone (such as the current time) while the phone is lying flat on a surface.

Something changes, though, once you start to combine “curved” with “flexible.” The new LG G Flex, for example, actually boasts a curved display that flexes and flattens out once you apply pressure to it: if you drop it, it can hypothetically flatten to absorb the blow. LG also says the curved display will create new types of entertainment experiences, similar to the IMAX viewing experience. (However, getting an IMAX experience on a 6-inch curved screen is ambitious.)

Where the innovation really starts to happen, though, is when you make the move from “curved” to “bended.” A Samsung patent for a “bended” screen shows what’s hypothetically possible, since a screen that extends over the edges of the phone actually does lend itself to a whole new series of user experiences. In a series of Samsung patent drawings, you can see how the whole user experience shifts – certain functions are pushed off the main display to the edges, freeing up more screen — while the extra screen real estate created by the bended edges can be used to display information about e-mail attachments or phone contact lists.

Where all this may be going, of course, is towards a future of not just “bended” but “bendable” computing —  a type of flexible computing that bends, shifts and adjusts to whatever we do in life. It could lead to breakthroughs in wearable computing by creating a fundamentally new type of computing that adapts to the shapes of our human bodies in motion. Or, it might lead to a type of computing that is foldable and stretchable, where things such as screen size will seem quaint – if you need more screen, you would simply stretch the screen. In slides that Samsung has released to analysts, a full spectrum of new functionality from fitness to fashion is made possible by moving from “curved” to “bended” to “flexible.”

Eventually, we may end up with something along the lines of the revolutionary PaperTab that was unveiled at this year’s CES show in Vegas — a flexible, paper-thin tablet that can be rolled up and unrolled, or flipped through like a stack of paper pages. Of course, it would be ironic if, after a period of massive innovation in smartphone technology – in which we now have more computing potential in the palm of our hand than they did during the Apollo space missions – we actually made it back full circle, to paper.