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Explainability has been a challenge in AI for as long as AI has existed. With the recently increased use of AI in society, it has become more important than ever that AI systems would be able to explain the reasoning behind their results also to end-users in situations such as being eliminated from a recruitment process or having a bank loan application refused by an AI system. Especially if the AI system has been trained using Machine Learning, it tends to contain too many parameters for them to be analysed and understood, which has caused them to be called `black-box' systems. Most Explainable AI (XAI) methods are based on extracting an interpretable model that can be used for producing explanations. However, the interpretable model does not necessarily map accurately to the original black-box model. Furthermore, the understandability of interpretable models for an end-user remains questionable. The notions of Contextual Importance and Utility (CIU) presented in this paper make it possible to produce human-like explanations of black-box outcomes directly, without creating an interpretable model. Therefore, CIU explanations map accurately to the black-box model itself. CIU is completely model-agnostic and can be used with any black-box system. In addition to feature importance, the utility concept that is well-known in Decision Theory provides a new dimension to explanations compared to most existing XAI methods. Finally, CIU can produce explanations at any level of abstraction and using different vocabularies and other means of interaction, which makes it possible to adjust explanations and interaction according to the context and to the target users.