These two handsets aren't official yet, but one company has taken a punt and guessed at what Apple has planned for its next models of iPhone.
The company is a Milan-based media agency called Set Solution, and it reckons Apple's iPhone 6C will have a curved screen, just like the LG Optimus G Flex.
But unlike the G Flex, the conceptual iPhone 6C has a flat back.
Set Solution has also mocked up an ultra-thin Apple handset, which is calls the iPhone Air. Well we've had the MacBook Air and iPad Air, so why not?
The 'C' in iPhone 6C stands for Curve, in Set Solution's video, though it shows the handset in similarly bright hues as the iPhone 5C.
The iPhone Air, meanwhile, has a wedge-shaped design, and is ridiculously thin. It measures up at just 1.5mm thick at the top, and 3mm at the base.
Set Solution reckons the iPhone Air will weigh 70g - that's a good 40g less than the iPhone 5S.
Both the iPhone 6C and iPhone Air will have Apple's Touch ID fingerprint sensor as well, so you can just touch the home button to unlock your phone.
Samsung also unveiled a curved phone recently, named the Samsung Galaxy Round. Unlike LG's Optimus G Flex, its screen curves from left to right, the idea being that you lay it on its back on a desk, and tip it up to see notifications.