We're still a long way from "strong AI". We need a few more ideas at least as good as deep learning. But it's a finite problem - biological brains work, DNA is about 4GB, and we have enough compute power in most data centers.

Right now we have enough technology to do a big fraction of what people do at work. That's the big economic problem.

General-purpose robots still seem to be a ways off. The next challenge there is handling of arbitrary objects, the last task done by hand in Amazon warehouses. Despite 30 years of work on the bin-picking problem, robots still suck at this in unstructured situations. Stocking a supermarket shelf, for example. Once that's solved, all the jobs that involve picking up something and putting it somewhere else gradually go away.

Rodney Brooks' Baxter was supposed to do this, but apparently doesn't do the hard cases. Amazon sponsored a contest for this, but all they got was a better vacuum picker. Work continues. This is a good YC-type problem.