Abstract:This paper surveys the application and development of Artificial Intelligence (AI) in Satellite Communication (SatCom) and Non-Terrestrial Networks (NTN). We first present a comprehensive list of use cases, the relative challenges and the main AI tools capable of addressing those challenges. For each use case, we present the main motivation, a system description, the available non-AI solutions and the potential benefits and available works using AI. We also discuss the pros and cons of an on-board and on-ground AI-based architecture, and we revise the current commercial and research activities relevant to this topic. Next, we describe the state-of-the-art hardware solutions for developing ML in real satellite systems. Finally, we discuss the long-term developments of AI in the SatCom and NTN sectors and potential research directions. This paper provides a comprehensive and up-to-date overview of the opportunities and challenges offered by AI to improve the performance and efficiency of NTNs.