Social media platforms mediate a significant fraction of human communication and attention. The impact of social media on society has been under increased scrutiny, and concerns over its effects have motivated varied and sometimes contradictory government regulation around the world. In this review article, we offer two ways of mapping the space of social media regulation: viewing social media either (i) as an architecture impacted by design choices, or (ii) as a market governed by incentives. We survey the most prominent regulatory approaches globally (both enacted and proposed), with an emphasis on the United States and the European Union, and position these options within the two maps. We conclude by discussing the fundamental trade-offs associated with different interventions, comparing jurisdictions, and highlighting paths forward in the context of the potentially-conflicting rights and interests of relevant stakeholders.