Rethinking the regulation of advertising-based platform business models such as Facebook/Meta and Google/Alphabet, which I call attention platforms, is an urgent task. Two decades of regulatory apathy and intellectual fragmentation have produced siloed approaches to the regulation of data and content that leave many urgent political, economic and environmental issues unaddressed. In this paper, I argue that current approaches to regulating data and datafication – approaches that regulate control over personal data or that focus on regulating social data – fail to address the most pervasive forms of extraction and harm in the attention platform economy: those that stem from addiction, over-consumption, virality, and fragmentation of the public sphere. Facilitating the emergence of just attention infrastructures, rather than just data infrastructures, should be a priority. This, I argue, requires a move toward more horizontal power to determine attention infrastructures, just advertising and funding systems and attention minimization measures, that is friction and incentives against attention capture.