Children are considered particularly important in debates about the possibilities and dangers of information and communication technologies (ICT). Discourses on ICT contain paradoxical representations of childhood. On the one hand, unlike most other understandings of child/adult relations, these discourses assume children to be equally, if not more, technologically competent than adults. On the other hand, children's very competence at using ICT is alleged to be putting them “at risk” of abuse or corruption. This paper addresses these moral panics about children and ICT by exploring to what extent and why parents are concerned about their children's safety in on-line space. In doing so the paper reflects on the extent to which anxieties about children in cyberspace replicate concerns about public outdoor space and the way networked computers emerge as different tools in different households.