It is well-known that there are serious issues with opaque methods in AI, including artificial neural networks (ANNs), when these are used to support human decision-making. As a consequence considerable efforts are being devoted to explainable AI, in general and based on ANNs. However, most of the existing proposals are on rendering the underlying AI methods interpretable (i.e. understandable to experts), rather than genuinely explainable to human stakeholders of different backgrounds. Meanwhile, several efforts are being devoted to genuinely explaining several forms of AI and other algorithms by using mappings from them into forms of so-called computational argumentation, leveraging on the amenability of argumentation to humans and to progress in developing computational argumentation tools within AI. To date, mappings into argumentative explanations from recommender systems and directly from data have been studied. This project aims to study ANNs of various kinds, and methods to make them interpretable, to build argumentative explanations for a variety of datasets and forms of ANNs, and develop a methodology for genuinely explainable, rather than just interpretable, ANNs.