As someone who works in the area, this provides a decent summary of the most popular research items. The most useful and impressive part is the set of open problems at the end, which just about covers all of the main research directions in the field.

The skepticism I'm seeing in the comments really highlights how little of this work is trickling down to the public, which is very sad to see. While it can offer few mathematical mechanisms to infer optimal network design yet (mostly because just trying stuff empirically is often faster than going through the theory, so it is more common to retroactively infer things), the question "why do neural networks work better than other models?" is getting pretty close to a solid answer. Problem is, that was never the question people seem to have ever really been interested in, so the field now has to figure out what questions we ask next.