If you want to buy a nearly bezel-free iPhone during this Apple (AAPL 0.94%) iPhone product cycle, then your only real choice will be the iPhone X, which starts at $999. Apple's lower-cost iPhones -- iPhone 8 and iPhone 8 Plus -- retain the same relatively large side, top, and bottom bezels that have been characteristic of the iPhone since the launch of the iPhone 6 series in September of 2014.
Next year, Apple is expected to introduce a next-generation iPhone X with the same 5.85-inch screen size as this year's model, as well as a larger version with a 6.46-inch display. Those phones should, too, be nearly bezel-free.
Apple is also expected to release an iPhone with a 6-inch liquid crystal display (LCD). Not much is known about this device, but I expect it to be the cheapest of the flagship iPhones that Apple introduces next year.
Though I suspect that the pricier iPhone X phones will still look sleeker than next year's LCD iPhone, I'm confident that Apple will dramatically improve the aesthetics of the LCD model by dramatically shrinking the bezels.
The question that I'd like to explore, then, is the following: How will Apple pull it off?
I see two options.
Touch ID elsewhere
If Apple dramatically reduces the size of the bezels of the 6-inch LCD iPhone, then it's likely that the iconic home button will need to be removed (as it has been in this year's iPhone X).
If the home button is removed and Apple continues to use Touch ID for biometric authentication, then it will need to relocate the Touch ID sensor.
One option for such a relocation would be the back of the phone, which is what several other Android-based smartphone makers have done. While this solution would be viable, it would arguably make the back of the device look significantly worse than the backs of the iPhone 8 and iPhone 8 Plus do.
I think this option isn't too likely.
Alternatively, Apple could try to embed the Touch ID scanner into, as has been suggested in the past, the power button. Patently Apple, for example, spotted an Apple patent filing describing just that.
Touch ID in the power button would certainly allow Apple to sidestep the aesthetic issues that a fingerprint scanner on the back would create, but it could be difficult to implement and it's not clear if the user experience of such an implementation would be good.
TrueDepth camera
Instead of trying to implement Touch ID in the 6-inch LCD iPhone, Apple could implement the TrueDepth camera subsystem, which would allow Apple to ditch Touch ID for Face ID.
The TrueDepth camera system is likely to add more cost to the LCD iPhone than a Touch ID fingerprint sensor would. Moreover, since the TrueDepth camera system requires a significant amount of space (which is why the current iPhone X has what people refer to as the notch cut out of the top of the display), Apple would likely need to retain a relatively large amount of top bezel to accommodate the technology.
For symmetry purposes, Apple would also need to retain a significant amount of bezel on the bottom of the device as well -- partially defeating the purpose of the home button/Touch ID removal.