Despite the rapid growth in attention on eXplainable AI (XAI) of late, explanations in the literature provide little insight into the actual functioning of Neural Networks (NNs), significantly limiting their transparency. We propose a methodology for explaining NNs, providing transparency about their inner workings, by utilising computational argumentation (a form of symbolic AI offering reasoning abstractions for a variety of settings where opinions matter) as the scaffolding underpinning Deep Argumentative eXplanations (DAXs). We define three DAX instantiations (for various neural architectures and tasks) and evaluate them empirically in terms of stability, computational cost, and importance of depth. We also conduct human experiments with DAXs for text classification models, indicating that they are comprehensible to humans and align with their judgement, while also being competitive, in terms of user acceptance, with existing approaches to XAI that also have an argumentative spirit.