In this paper, I approach the power of digital platforms by using the republican concept of domination. More specifically, I argue that the traditional, agent-relative interpretation of domination, in the case of digital domination, is best supplemented by a more radical version, on which republicans ought to give priority to structural elements. I show how radical republicanism draws attention to (1) the economic rationales and the socio-technical infrastructures that underlie and support digital platforms and to (2) the forms of influence (...) that are directed at cognitive dimensions, such as habituation and routinisation, which are particularly relevant for the power of digital platforms. These insights also imply that republicans have reason to favour a more structural response to digital platforms over more direct and individualised forms of control that fit with a ‘standard’ republican approach, such as securing exit options and requiring user consent. (shrink)