In this special issue, we ask: What do we see when we look at datafied societies through the lens of care? Following the footsteps of feminist writers, activists, and academics who take care as a vantage point for scrutinising and reimaging technoscientific societies, this special issue brings together scholars from critical data studies who explore what we might learn (and see) when we apply care ethics to the study of datafication. To develop a view on datafied societies informed by ethics, concepts, and practices of care, we propose a move from critique to care in social studies of data-driven technologies. We specifically identify five moves in which a care lens provides a new perspective when studying datafication and datafied societies: (1) a move from data-driven technologies to socio-digital care arrangements, (2) a move from data science to data work and care, (3) a move from technical to situated modes of knowledge production, (4) a move from studying harms of datafication to the politics of vulnerability, and (5) a move towards building communities of care. Discussing how critical data studies and care ethics can mutually contribute to each other, this collection explores how this way of thinking can inform new ways of seeing datafied societies and imagine living and being well in more than human worlds nurtured by care.