The rapid advancement of artificial intelligence (AI) technology has catalyzed unprecedented innovation in the healthcare industry, transforming medical practices and patient care. However, this progress brings significant ethical challenges, highlighting the need for a comprehensive exploration of algorethics—the intersection of algorithm design and ethical considerations. This study aimed to conduct a narrative review of reviews in the field of algorethics with specific key questions. The review utilized a standardized checklist for narrative reviews, including the ANDJ Narrative Checklist, to ensure thoroughness and consistency. Searches were performed on PubMed, Scopus, and Google Scholar. The review revealed a growing emphasis on integrating fairness, transparency, and accountability into AI systems, alongside significant progress in ethical AI development. The importance of collaboration between different domains of scientific production, such as social sciences and standardization (like the IEEE), and the development of guidelines is significantly emphasized, with demonstrated direct impact in the health domain. However, gaps persist, particularly in the lack of standardized evaluation methods and the challenges posed by complex sectors like healthcare. The findings underscore the need and importance for robust data governance to prevent biases and highlight the importance of cross-disciplinary collaboration in creating comprehensive ethical frameworks for AI. The field of algorethics has important applications in the health domain, and there is a significant increase in attention, with a focus on addressing issues and seeking both practical and theoretical solutions. Future research should prioritize establishing standardized evaluation practices for AI, fostering interdisciplinary collaboration, developing sector-specific ethical guidelines, exploring AI’s long-term societal impacts, and enhancing ethical training for developers. Continued attention to emerging ethical standards is also crucial for aligning AI technologies with evolving ethical principles.