Individuals and communities increasingly depend on, and fill their lives with, machine cultures, in the form of both interfaces and infrastructures. This global push for machine cultures has given rise to an increasing demand for data and engendered a proliferation of public, private and public-private dataset repositories. While datasets form a foundational element of machine cultures, they rarely come into focus as objects of critical study. But in recent years a critical discursive formation on datasets has begun to emerge, which disturbs the idea of datasets as operational instruments of digital knowledge production and seek to instead ‘bring people back in’. The present article identifies these preliminary explorations as ‘critical dataset studies’ and draws on critical archival studies to articulate the ethico-political surfaced by these studies. Specifically it argues that critical dataset studies shows the need for an expanded ethical and conceptual approach to datasets that not only relies on linear notions of deletion and accountability but also on iterative frameworks of remains and response-ability.