This article surveys the use of algorithmic systems to support decision-making in the public sector. Governments adopt, procure, and use algorithmic systems to support their functions within several contexts -- including criminal justice, education, and benefits provision -- with important consequences for accountability, privacy, social inequity, and public participation in decision-making. We explore the social implications of municipal algorithmic systems across a variety of stages, including problem formulation, technology acquisition, deployment, and evaluation. We highlight several open questions that require further empirical research.