I think we can expect advances on two fronts, software and hardware. The software we enjoy today is the product of various software object libraries that do many things; I believe neural net libraries are currently being developed that do various things as thoughtfunk mentioned of Deep Learning. And there are several AI engines being trained for various tasks. As hardware improves one AI engine will be capable of learning more, and multiple network objects will be combined, for example sight, hearing, motor control, smell, medical expertise, biochemistry, etc. It seems likely that a single AI network will be capable of learning all scientific knowledge, but perhaps there is some as yet unknown limit.
I think the three laws of robotics may be taught an AI as any other lesson. However, whether we can compel an AI to obey them or any human law is an open question. We are working with computers, but they will be smart and may be able to circumvent anything we try to make compelling.