If you've seen photos from any technology trade show in the last decade, you've probably seen someone showing off a flexible screen. It makes for a nice demo, but a real product? According to Bloomberg, Samsung is planning to launch not one but two phones in 2017 with foldable screens.
This rumor comes from the always popular "people familiar with the matter." These mysterious people say that Samsung is planning a device with a screen that folds in half like a compact or a flip phone. The other device has a 5-inch screen, but can fold out to become an 8-inch tablet. It's not clear how that would work.
Samsung is the world's largest maker of OLED panels, and I think it's obvious they make the best as well. If anyone can do this, it's Samsung. It has demoed flexible panels a few times in recent years. Still, for an actual phone it all sounds like science fiction nonsense right now without additional details. Even if it's possible to make a folding phone, it might not be a good idea. Samsung did make the Galaxy Round, so I guess anything is possible.