Recent developments in Artificial Intelligence (AI) have generated great expectations for the future impact of AI in education and learning (AIED). Often these expectations have been based on misunderstanding current technical possibilities, lack of knowledge about state-of-the-art AI in education, and exceedingly narrow views on the functions of education in society. In this article, we provide a review of existing AI systems in education and their pedagogic and educational assumptions. We develop a typology of AIED systems and describe different ways of using AI in education and learning, show how these are grounded in different interpretations of what AI and education is or could be, and discuss some potential roadblocks on the AIED highway.