We have seen literally nothing substantial (like actually photos, etc.) about Samsung's upcoming flexible display smartphone, but it continues to be talked about in the media, specially since a Samsung officially reportedly confirmed its existence. We had heard that it would be announced this week, and now the Korean media is confirming that the device will be called the Galaxy Round and will indeed be announced before the week is over.
Galaxy Round isn't exactly something you'd want to name your smartphone, so that is likely a temporary name Samsung is using to keep leaks at bay. The device will use a screen that is made of a plastic substrate instead of glass, giving it higher longevity and reducing manufacturing costs. The specs are expected to be similar to the Note 3's, though a recent rumor suggested it might be based on the Galaxy S3.
The Galaxy Round will reportedly be priced very high as Samsung is looking to manufacture it in only limited quantities, though the price might come down if the Galaxy Round doesn't support stylus functionality.