During the last decade there has been burgeoning research concerning the ways in which we should think of and apply the concept of responsibility for Artificial Intelligence. Despite this conceptual richness, there is still a lack of consensus regarding what Responsible AI entails on both conceptual and practical levels. The aim of this paper is to connect the ethical dimension of responsibility in Responsible AI with Aristotelian virtue ethics, where notions of context and dianoetic virtues play a grounding role for the concept of moral responsibility. The paper starts by highlighting the important difficulties in assigning responsibility to either technologies themselves or to their developers. Top-down and bottom-up approaches to moral responsibility are then contrasted, as we explore how they could inform debates about Responsible AI. We highlight the limits of the former ethical approaches and build the case for classical Aristotelian virtue ethics. We show that two building blocks of Aristotle’s ethics, dianoetic virtues and the context of actions, although largely ignored in the literature, can shed light on how we could think of moral responsibility for both AI and humans. We end by exploring the practical implications of this particular understanding of moral responsibility along the triadic dimensions of ethics by design, ethics in design and ethics for designers.