Intensifying concerns about online platform firms’ rapid rise, expansion, and growing asymmetric power have attracted political scrutiny and undermined the legitimacy of a minimalist regulatory regime that is giving way to intense debate and increasingly interventionist governmental policies and enforcement actions. First, we view the rise of, and recent political responses to, the often-predatory power and manipulative conduct of platform firm in terms of a ‘Polanyian’ double movement in which the destabilising and destructive effects of unchecked corporate activities and market development eventually generates political and regulatory responses to constrain private power that threaten the social, political, and economic order. Second, incipient legal changes, most notably the EU’s proposed Digital Markets Act and Digital Services Act, indicate a shift in regulatory emphasis from competition (and antitrust) policy and law towards more intensive and encompassing forms of socio-economic regulation. Finally, these regulatory changes will likely vary in character and significance across political jurisdictions, and embody distinctive and possibly divergent developmental trajectories. The EU may have a first-mover advantage in regulating platform firms, but we are only at the very beginning of a protracted and conflictual transformational process.