While I am getting up to speed (a slow process, given my other commitments), there is no reason for someone who is interested in this topic to zoom to the cutting edge. A good place for a jump start, after you have read On Intelligence, is the Numenta web site. You can also check out the OnIntelligence.org web site, which sponsors some forums on Hawkins's predictive memory model of intelligence and has some links to related materials. Today I'll just describe what is at the Numenta site.
If you have not read On Intelligence, in particular Chapter 6, "How the Cortex Works," you can still get a lot out of reading materials at the Numenta site. However, I would advise reading the book first, old fashioned as that may sound.
You might be ready to jump right into "Hierarchical Temporal Memory Concepts, Theory and Terminology" by Jeff Hawkins and Dileep George. You are going to want to read it at some point. It is focused on HTMs (Hierarchical Temporal Memory technology). This is an attempt to implement the model of the human brain cortex, but in data-processing rather than biological terms. It is also the main technology being developed at Numenta.
On the other hand you may want to look at the HTM Technology Overview first. It is short and sweet, and also has a link to Problems That Fit HTMs. Of course if the HTM actually is a good model for the human cortex, HTMs should do well at problems that people (and often other mammals) do well at, but that computers, even using AI (artificial intelligence) techniques are not good at.
If you are a hands-on person, you could skip the theory and start with one of the software development kits. One is Vision Software, the other is NuPIC which now includes Vision. However, the NuPIC web page has a link to technical resources that would be important if you get serious about working with HTMs.
I'll write more about Numenta, just as I'll be writing more commentary on machine understanding and intelligence in general. I will be approaching HTMs from a critical perspective: do they implement a predictive memory model; is this the best implementation; and is the model really central to biological intelligence and machine understanding.