The Internet enables the free flow of information on an unprecedented scale but increasingly the management of individuals’ fundamental rights, such as privacy and the mediation of free expression, is left in the hands of private actors. The popularity of a few web platforms across the globe confers on the providers both great power and heavy responsibilities. An underlying tension exists for those companies between self-regulation and being held accountable for rights violations by states. Solutions might include provision of paid alternatives, more sophisticated definition and handling of different types of data and all stakeholders' cooperation in developing realistic and robust processes for content moderation that comply with the rule of law.