This article presents a mapping review of the literature concerning the ethics of artificial intelligence (AI) in health care. The goal of this review is to summarise current debates and identify open questions for future research. Five literature databases were searched to support the following research question: how can the primary ethical risks presented by AI-health be categorised, and what issues must policymakers, regulators and developers consider in order to be 'ethically mindful? A series of screening stages were carried out-for example, removing articles that focused on digital health in general (e.g. data sharing, data access, data privacy, surveillance/nudging, consent, ownership of health data, evidence of efficacy)-yielding a total of 156 papers that were included in the review.We find that ethical issues can be (a) epistemic, related to misguided, inconclusive or inscrutable evidence; (b) normative, related to unfair outcomes and transformative effectives; or (c) related to traceability. We further find that these ethical issues arise at six levels of abstraction: individual, interpersonal, group, institutional, and societal or sectoral. Finally, we outline a number of considerations for policymakers and regulators, mapping these to existing literature, and categorising each as epistemic, normative or traceability-related and at the relevant level of abstraction. Our goal is to inform policymakers, regulators and developers of what they must consider if they are to enable health and care systems to capitalise on the dual advantage of ethical AI; maximising the opportunities to cut costs, improve care, and improve the efficiency of health and care systems, whilst proactively avoiding the potential harms. We argue that if action is not swiftly taken in this regard, a new 'AI winter' could occur due to chilling effects related to a loss of public trust in the benefits of AI for health care.