This report first takes stock of XAI-related requirements appearing in various EU directives, regulations, guidelines, and CJEU case law. This analysis of existing requirements will permit us to have a clearer vision of the purposes, the ``why'', of XAI, which we separate into five categories: contestability, empowerment/redressing information asymmetries, control over system performance, evaluation of algorithmic decisions, and public administration transparency. The analysis of legal requirements also permits us to create four categories of recipients for explainability: data science teams; human operators of the system; persons affected by algorithmic decisions, and regulators/judges/auditors. Lastly, we identify four main operational contexts for explainability: XAI for the upstream design and testing phase; XAI for human-on-the-loop control; XAI for human-in-the-loop control; and XAI for ex-post challenges and investigations.Second, we will present user-centered design methodology, which takes the purposes, the recipients and the operational context into account in order to develop optimal XAI solutions.Third, we will suggest a methodology to permit suppliers and users of high-risk AI applications to propose local XAI solutions that are effective in the sense of being ``meaningful'', for example, useful in light of the operational, safety and fundamental rights contexts. The process used to develop these ``meaningful'' XAI solutions will be based on user-centric design principles examined in the second part.Fourth, we will suggest that the European Commission issue guidelines to provide a harmonised approach to defining ``meaningful'' explanations based on the purposes, audiences and operational contexts of AI systems. These guidelines would apply to the AI Act, but also to the other EU texts requiring explanations for algorithmic systems and results.