Debates about the prospective clinical use of polygenic risk scores (PRS) have grown considerably in the last years. The potential benefits of PRS to improve patient care at individual and population levels have been extensively underlined. Nonetheless, the use of PRS in clinical contexts presents a number of unresolved ethical challenges and consequent normative gaps that hinder their optimal implementation. Here, we conducted a systematic review of reasons of the normative literature discussing ethical issues and moral arguments related to the use of PRS for the prevention and treatment of common complex diseases. In total, we have included and analyzed 34 records, spanning from 2013 to 2023. The findings have been organized in three major themes: in the first theme, we consider the potential harms of PRS to individuals and their kin. In the theme “Threats to health equity,” we consider ethical concerns of social relevance, with a focus on justice issues. Finally, the theme “Towards best practices” collects a series of research priorities and provisional recommendations to be considered for an optimal clinical translation of PRS. We conclude that the use of PRS in clinical care reinvigorates old debates in matters of health justice; however, open questions, regarding best practices in clinical counseling, suggest that the ethical considerations applicable in monogenic settings will not be sufficient to face PRS emerging challenges.