Organoids are 3D structures grown from pluripotent stem cells derived from human tissue and serve as in vitro miniature models of human organs. Organoids are expected to revolutionize biomedical research and clinical care. However, organoids are not seen as morally neutral. For instance, tissue donors may perceive enduring personal connections with their organoids, setting higher bars for informed consent and patient participation. Also, several organoid sub-types, e.g., brain organoids and human–animal chimeric organoids, have raised controversy. This systematic review provides an overview of ethical discussions as conducted in the scientific literature on organoids. The review covers both research and clinical applications of organoid technology and discusses the topics informed consent, commercialization, personalized medicine, transplantation, brain organoids, chimeras, and gastruloids. It shows that further ethical research is needed especially on organoid transplantation, to help ensure the responsible development and clinical implementation of this technology in this field.