Public organizations are increasingly using automated decision-making (ADM) as a means for improving efficiency. The automation, however, risk undermining their legitimacy if not carefully constructed to preserve public values. This paper aims to provide a synthesis and analysis of literature on ADM in the public sector from various disciplines. We illustrate dominant themes in the public sector ADM literature and unveil areas that require further research. We call for (1) fine-grained conceptualizations of ADM, that accommodate differences in e.g., types of decisions and levels of government; (2) further attention to decision-making hybrids, where both humans and algorithms have agency, and how such hybrids should be developed to avoid biases; and (3) preventive safeguards that protect individual rights while ensuring the public interest in transparency. We thus contribute with an overview of the dominant themes in the public sector ADM literature, and directions for future research on this topic.