While many forms of data-driven surveillance are now a ‘fact’ of contemporary life amidst datafication, obtaining concrete knowledge of how different institutions exploit data presents an ongoing challenge, requiring the expertise and power to untangle increasingly complex and opaque technological and institutional arrangements. The how and why of potential surveillance are thus wrapped in a form of continuously produced uncertainty. How then, do affected groups and individuals determine how to counter the threats and harms of surveillance? Responding to an interdisciplinary (...) concern with agency amidst datafication, this article explores what I term ‘anticipatory data practices’ – future-oriented practices which provide a concrete anchor and a heuristic for action amidst the persistent uncertainties of life with data. This article traces how anticipatory data practices have emerged within civil society practices concerned with countering the harms of surveillance and data exploitation. The mixed-method empirical analysis of this article draws from 50 interviews with digital security educators and technology developers; participant observation at 12 civil society events between 2016 and 2019 and the textual analysis of 100 security manuals produced by NGOs and grassroots groups. (shrink)