The European Union was founded upon a vision of a socially responsible, free market-based economy unencumbered by the political and economic concentrations of power that contributed to the Second World War. The challenges of globalization and digitization may, though, be pushing that vision to the limit. In particular, there is growing concern that technological development has come alongside increased concentration of power, rising inequality, invasion of privacy, a loss of meaningful employment, the destruction of the environment, climate change and the erosion of democracy. Attention has turned to competition law’s accountability for these apparent market and societal failures, with a particular focus on digital markets. Academics, international enforcers, legislators and US presidential hopefuls have variously argued that competition laws cannot cope with the perceived challenges raised by the digital economy. In response, governments across the globe have commissioned reports on whether and how competition law should be reformed to address these challenges. And ambitious legislative initiatives have been proposed to regulate the behavior of digital platforms, including in the EU, Germany and the UK.