If you're looking to get weird with your phone, the curved screen of the official Samsung Galaxy Round is a good start. Well, sort of. The curved 5.7-inch screen—same as the uncurved Note 3—is a real thing that Samsung is actually making but it's only launching on SK Telecom in South Korea.
There doesn't seem to be any real sensible justification for a curved screen (for the time being, at least) other than hey, look at this weird technology that exists on my phone. That's not stopping Samsung from marketing the Round's 'roll effect' as a feature though. You basically roll the phone to wake the screen to see the time and your notifications. I guess that's sort of justifying the curved screen but still, baaaaaarely: