Several companies and organizations have started to work on projects that are trying to emulate the human brain, and all are doing it in different ways. One of the companies working on this sort of project is Qualcomm, who's trying to develop a neuromorphic processor, that doesn't need any programming or instructions, and it can just learn to do things itself, just like a human brain would.
Qualcomm is hoping to release this chip for commercial purposes next year, but only as the next step in its development. You won't actually see this processor powering your phone's AI anytime soon. Even if you will see it in the next few years, it won't be replacing your general-purpose CPU, but instead be used as a co-processor to perform actions "that humans do with ease: see, speak, listen, navigate, manipulate and control."
These sort of co-processors could become much more accurate for facial recognition, voice recognition, navigation and planning, and so on, which right now requires very complex programming to do even relatively well (but not perfect). Humans are much better at identifying faces for example, and we "just do it". If we can get computers to act the same way, certain tasks could be performed a lot easier and more efficiently.
We've already seen that both Google and Apple are interested in these sort of co-processors. Google has been trying for years to write software and AI that can recognize images and objects inside images better, and they've recently launched the Moto X with a co-processor for voice recognition and one for contextual computing. In the same way, Apple has implemented a co-processor that better identifies movement, in their chips.
IBM has also recently announced a brain-like super-computer that only has about 10 percent the number of neurons of a human brain, but is 1,500 times slower, and uses several MW of power, compared to just 20W for the human brain. IBM believes it will take another 50 years or so before they can build something that is as powerful as the human brain, as efficient, and in a package just as small that can fit on a desk. Until then we're still going to see big improvements in co-processors that do one thing really well, and improve the capabilities of our devices dramatically. We still have to get to 64-bit processors first, though.