Artificial intelligence (AI) has the potential to transform both the practice of law and academic reflection on law. However, the technology is still at a very early stage and there are signigificant limitations on what can be achieved. In this paper, I will briefly sketch the state of the art of applications of machine learning to predicting outcomes of court cases, chiefly in Canada and in the United States. I will then focus on the challenges of this kind of research in UK law (like access to texts of court judgments). Finally, I will discuss the “proof of concept” project I developed on predicting case outcomes in a small area of UK public law.