The purpose of this paper is to critically analyse digital society from the perspective of dilemmatic space. The theoretical frame offers new ways of making sense of the digital society, and may provide new perspectives on how to manoeuvre (or not) in it. The theoretical framework is applied in relation to three themes of digitalised society: (a) the blogosphere and social networking communities (SNC), (b) file sharing, network control and surveillance; and (c) educational school context. These themes have been chosen in order to illustrate the different aspects of a digital society and to show how the theoretical framework operates when different aspects of these themes are placed in the foreground or background, i.e. emphasised or downplayed.