Samsung is obviously not the only company working on the technology. LG, Philips, Sharp, Sony and Nokia are all working on flexible displays, but the word is that Samsung will be the first to actually ship the displays in products, and it could happen next year. According to the report, LG has already begun mass producing flexible e-ink displays, but Samsung could be the first to make a flexible smartphone display, likely using Samsung's favorite OLED tech.
Of course, we still don't have flexible motherboards, or flexible batteries, so don't expect fully flexible phones just yet. But, flexible displays would definitely end that whole problem that we saw with the iPhone 4/4S, and that the Nexus 4 is having with cracked glass. Flexible displays are said to be virtually unbreakable.