The author reviews the research and scholarly literature about young children's play with tablet computers and identifies four major topics relevant to the subject--digital literacy, learning, transgressive and creative play, and parental involvement. He finds that young children's tablet computer play relies not only on technology, but also on sociocultural conditions. He argues that research should pay greater attention to transgressive play and should in general treat play as an autotelic concept because the nuances of play are as important as its function. He calls attention to the lack of affordances for creativity in apps for young children, explores the need for parental involvement in young children's tablet computer play, and discusses the importance of agency and access in such play.