The current generation of young children has been described as "digital natives", having been born into a ubiquitous digital media environment. They are envisaged as educationally independent of the guided interaction provided by "digital immigrants": parents and teachers. This article uses data from the Longitudinal Study of Australian Children (LSAC) to study the development of vocabulary and traditional literacy in children aged from 0 to 8 years; their access to digital devices; parental mediation practices; children's use of digital devices as recorded in time-diaries; and, finally, the association between patterns of media use and family contexts on children's learning. The analysis shows the importance of the parental context in framing media use for acquiring vocabulary, and suggests that computer (but not games) use is associated with more developed language skills. Independently of these factors, raw exposure to television is not harmful to learning. (Contains 4 tables.)