Artificial intelligence (AI) is being applied in medicine to improve healthcare and advance health equity. The application of AI-based technologies in radiology is expected to improve diagnostic performance by increasing accuracy and simplifying personalized decision-making. While this technology has the potential to improve health services, many ethical and societal implications need to be carefully considered to avoid harmful consequences for individuals and groups, especially for the most vulnerable populations. Therefore, several questions are raised, including (1) what types of ethical issues are raised by the use of AI in medicine and biomedical research, and (2) how are these issues being tackled in radiology, especially in the case of breast cancer? To answer these questions, a systematic review of the academic literature was conducted. Searches were performed in five electronic databases to identify peer-reviewed articles published since 2017 on the topic of the ethics of AI in radiology. The review results show that the discourse has mainly addressed expectations and challenges associated with medical AI, and in particular bias and black box issues, and that various guiding principles have been suggested to ensure ethical AI. We found that several ethical and societal implications of AI use remain underexplored, and more attention needs to be paid to addressing potential discriminatory effects and injustices. We conclude with a critical reflection on these issues and the identified gaps in the discourse from a philosophical and STS perspective, underlining the need to integrate a social science perspective in AI developments in radiology in the future.