According to new rumors, Samsung plans to release a smartphone in 2014 that will feature a three-sided display. This is a YOUM OLED display that wraps around the edges, probably similar to the prototypes the company showed at CES 2013:
According to the rumors, the phone will be released in 2014 (probably the second half of the year). Samsung hasn't decided yet whether this will be a Galaxy Note phone, or a Galaxy S one, or an altogether new class of phones.
Currently Samsung produces 5.7" Full-HD flexible (plastic-based) AMOLED displays (as used in the Galaxy Round). It's likely that the 3-sided display will have a different resolution -and size - as the display is actually wider than usual. The idea with the display on the side is that you can show notifications, or even use the area for soft-buttons UI.