According to a report from Reuters, Apple will be buying OLED display panels for future iPhones from both Samsung and LG. The companies are apparently "close to a final agreement," though the screens might not actually make it into a shipping iPhone until 2018 (that would be the year Apple introduces the iPhone 8, if current trends continue).
While these supplier deals don't always work out, the move would make sense for Apple. The LCD panels that the company currently uses need to be fully lit whenever you turn the screen on, no matter what you're actually looking at. The primary benefit of OLED panels is that you only have to light up the individual pixels that are being used to display the image—anything that's black doesn't need to be lit, which improves contrast and reduces power consumption.
For years, the technology has had other drawbacks. Early OLED screens suffered from poor outdoor visibility, greenish or purplish whites, and over-saturated, inaccurate colors. But as recent analyses of Samsung Galaxy phone displays have shown, the screen technology has mostly closed the gap in the last couple of years, delivering the benefits of OLED with fewer compromises.