This paper offers a new characterisation of young children's (2-8 years) reading for pleasure (RfP) with digital books. This characterisation is rooted in a re-contextualisation of Anna Craft's conceptualisation of twenty-first century childhoods in "Creativity and education futures" (Stoke on Trent, Trentham, 2011) and a review of the literature concerning young children's RfP with digital books. The paper develops Craft's (2011) work by considering the ways in which digital books can resource the "4Ps of digital childhood" in reading for pleasure. Six facets of reader engagement, nested within Craft's (2011) 4Ps, are presented: affective, creative, interactive, shared, sustained and personalised reading engagements. It is argued that this characterisation of young children's reading engagements can enrich our understanding of the affordances of digital books in relation to RfP in the twenty-first century. The paper thus offers an important new contribution, going beyond established work in the field, which typically explores digital books in relation to children's learning, product design or developmental outcomes.