This article explores the ways in which what we call the analogue and the datafied mindsets perceive the functioning of the datafied world. Based on a qualitative interview study of two generations of media users in Estonia, Portugal, and Sweden, we present and analyze underlying patterns in participants’ media attitudes and related practices. We show that belonging to a media generation does not always produce a homogeneous mindset or a uniform attitude toward media technologies. These mindsets, being ideal-typical constructs, are not bound to individuals: the same person can display features of the analogue and the datafied mindset in relation to different parts of the datafied world. One mindset does not replace the other but rather adds another layer to the social action of the individuals. The mindsets are multi-dimensional and molded by contrasting understandings, indicating that the tenacious structures of the analogue world linger on in the datafied social space.