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Air Traffic Management (ATM) will be more complex in the coming decades due to the growth and increased complexity of aviation and has to be improved in order to maintain aviation safety. It is agreed that without significant improvement in this domain, the safety objectives defined by international organisations cannot be achieved and a risk of more incidents/accidents is envisaged. Nowadays, computer science plays a major role in data management and decisions made in ATM. Nonetheless, despite this, Artificial Intelligence (AI), which is one of the most researched topics in computer science, has not quite reached end users in ATM domain. In this paper, we analyse the state of the art with regards to usefulness of AI within aviation/ATM domain. It includes research work of the last decade of AI in ATM, the extraction of relevant trends and features, and the extraction of representative dimensions. We analysed how the general and ATM eXplainable Artificial Intelligence (XAI) works, analysing where and why XAI is needed, how it is currently provided, and the limitations, then synthesise the findings into a conceptual framework, named the DPP (Descriptive, Predictive, Prescriptive) model, and provide an example of its application in a scenario in 2030. It concludes that AI systems within ATM need further research for their acceptance by end-users. The development of appropriate XAI methods including the validation by appropriate authorities and end-users are key issues that needs to be addressed. Full article