This paper concerns children's relations with the geological aspects of digital media technologies. Using ideas from media theory, I develop a new conceptual framework for childhood studies research on digital media that goes beyond the dominant focus on children's use of technology. I argue that studies of use would benefit from being linked up with analyses of the technicality and physicality of technology. Following recent debates concerning the Anthropocene, the planetary nature of digital media require analyses that link local and global scales, and address the politics of the specific materialities of digital media. As an example of the analytical potential of this approach, I discuss the issue of child labour in cobalt mining in the Democratic Republic of Congo.