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Explainable AI (XAI) has been investigated for decades and, together with AI itself, has witnessed unprecedented growth in recent years. Among various approaches to XAI, argumentative models have been advocated in both the AI and social science literature, as their dialectical nature appears to match some basic desirable features of the explanation activity. In this survey we overview XAI approaches built using methods from the field of computational argumentation, leveraging its wide array of reasoning abstractions and explanation delivery methods. We overview the literature focusing on different types of explanation (intrinsic and post-hoc), different models with which argumentation-based explanations are deployed, different forms of delivery, and different argumentation frameworks they use. We also lay out a roadmap for future work.