Within the general excitement about artificial intelligence, there has been special interest in the technology’s application to discovery of scientific knowledge. Like AI itself, this subfield has a long history and many successes, but also outstanding challenges. In this talk, I focus on two problems that have received considerable attention: discovery of numeric equations and construction of qualitative process models. In each case, I define the computational task, review basic approaches, and report successes that led to scientific insights. After this, I turn to a third paradigm – inductive process modeling – that moves beyond earlier efforts to generate quantitative explanations of scientific data in terms of domain knowledge. I present multiple approaches to this problem, present encouraging results, and discuss open issues that merit further attention from the AI community.