Writing is part and parcel of children's active meaning-making on and with screens, but it has been relatively neglected in the literature focused on children's digital literacies. This study synthesises existing empirical evidence focused on young children's (aged between 2 and 8 years) writing on screen and identifies the relationships between dominant themes in published literature and contemporary theories of children's technology use. A systematic literature review that included studies from diverse disciplines yielded 21 papers. Constant comparative analysis generated five themes that indicate four key directions for future research. We call attention to researchers' "theoretical framing" to supplement mono-disciplinary approaches and single levels of analysis. We suggest that future research should provide greater "specification of the purpose" of children's writing on screen and the different "types of tools and applications" supporting the activity. We also highlight the need for interdisciplinary approaches that would capture the composing stages involved in the writing process with and "around" screens. Finally, we point out possible "age-related differences" in documenting and reporting the composing process in classrooms. Overall, limitations in the current evidence base highlight the need for research conducted from a critical perspective and focused more directly on multimodality.