As social media have become vital channels for all kinds of political communication and cultural production, the regulation of social media content has also become a central arena for the contemporary politics of censorship. This chapter offers an overview of the functioning of algorithmic content moderation: the automated monitoring and filtering of user-generated content by online platforms, guided by their legal obligations, in-house content policies and commercial objectives. Given the concentrated power of a small number of multinational social media companies, many scholars consider that their de facto power to regulate users' speech represents a new and concerning form of private censorship. This power is also routinely leveraged by state authorities, through both formal legal obligations and various forms of more informal cooperation and influence. In this context, the chapter argues that public and private censorship cannot be clearly distinguished. Ultimately, all moderation of user content plays out against the backdrop of complex entanglements between public institutions and private companies. As such, moderation is alwaysmore or less directlyinfluenced by public policy, but also by platform companies' commercial objectives. To illustrate these dynamics, the chapter uses a well-publicised case in which Meta (owner of Facebook and Instagram) was revealed to be censoring drill music videos following informal requests from UK police. This case is used to illustrate some of the key political concerns raised by contemporary forms of algorithmic censorshipnotably including a lack of transparency and accountability mechanisms governing state intervention, and the replication in algorithmic decision-making software of institutional racism and other historic biases against marginalised groups. The chapter concludes by discussing how algorithmic moderation on social media is likely to develop in the future, highlighting some recent regulatory and technological developments which suggest that state and corporate control of online media will continue to intensify.