  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.
