School districts in the US and around the world are increasingly moving away from traditional neighborhood school assignment, in which pupils attend closest schools to their homes. Instead, they allow families to choose from schools within district boundaries. This creates a market with parental demand over publicly-supplied school seats. More frequently than ever, this market for school seats is cleared via market design solutions grounded in recent advances in matching and mechanism design theory. The literature on school choice is reviewed with emphasis placed on the trade-offs among policy objectives and best practices in the design of admissions processes. It is concluded with a brief discussion about how data generated by assignment algorithms can be used to answer contemporary empirical questions about school effectiveness and policy interventions.