Curved displays and cards
The new curved display smartphones from LG and Samsung have thus far failed to woo journalists and commenters alike, in part due to the lack of any cool new software features enabled by the technology. However, I do think that there's one use case that these curved displays would excel at:
Since conventional mobile app interfaces are often multiaxial in nature (i.e. multitouch gestures, navigating Maps, etc.), the use of curved displays in that context would often be disadvantageous.
However, the recent trend of card interfaces lends itself very to a curved display, seeing as they are often monoaxial à la Google Now. Thus, a phone curved along the vertical axis (Galaxy Round) would work well with horizontal cards interface (i.e. Facebook Home lock screen), and vice versa (i.e. Google Now) for a phone curved along the horizontal axis (G Flex).
Using this interaction paradigm, the curvature of the screen enable more natural scrolling, as the screen would guide the finger. All of this assumes that the use of Google Now or another contextual cards service surpasses the use of dedicated apps, or that the in-app cards could be served from the home screen, thus enabling the continuous monoaxial scrolling.