This article discusses the political economy of AI capitalism. It considers AI as a General Purpose Technology (GPT) and argues we need to investigate the power concentration of Big Tech. AI capitalism is characterised by the commodification of data, data extraction and a concentration in hiring of AI talent and compute capacity. This is behind Big Tech’s unstoppable drive for growth, which leads to monopolisation and enclosure under the winner takes all principle. If we consider AI as a GPT—technologies that alter society’s economic and social structures—we need to come up with alternatives in terms of ownership and governance. The commons is proposed as an alternative for thinking about how to organise AI development and how to distribute the value that can be derived from it. Using the commons framework is also a way of giving society a more prominent role in the debate about what we expect from AI and how we should approach it.