Massive Open Online Courses (MOOCs) have gained tremendous popularity in the last few years. Thanks to MOOCs, millions of learners from all over the world have taken thousands of high-quality courses for free. Putting together an excellent MOOC ecosystem is a multidisciplinary endeavour that requires contributions from many different fields. Artificial intelligence (AI) and data mining (DM) are two such fields that have played a significant role in making MOOCs what they are today. By exploiting the vast amount of data generated by learners engaging in MOOCs, DM improves our understanding of the MOOC ecosystem and enables MOOC practitioners to deliver better courses. Similarly, AI, supported by DM, can greatly improve student experience and learning outcomes. In this survey paper, we first review the state-of-the-art artificial intelligence and data mining research applied to MOOCs, emphasising the use of AI and DM tools and techniques to improve student engagement, learning outcomes, and our understanding of the MOOC ecosystem. We then offer an overview of key trends and important research to carry out in the fields of AI and DM so that MOOCs can reach their full potential.