There's a fascinating (if understandably promotional) post over on Qualcomm's site, in which the imaging capabilities of the upcoming smartphone chipset, the Snapdragon 835, are discussed. See below for a few quotes.
In summary, it's becoming increasingly evident that great smartphone imaging is just as much about processing power as it is about the raw optics and sensor size. The Nokia 808 PureView arguably started the trend, with a custom image processor, but with the likes of the modern Snapdragon 820/821 and now 835, we have even faster image processing and implemented so generically that it can be part of a great many devices and not just the one it was designed for.