While the dominating societal discourse highlights the positive aspects of digitalization of childhood, families with young children may perceive things differently, even demonstrating various forms of resistance to children’s media practices and use of digital technology. It is within the domestic sphere that young children are introduced to digital media, but still policymakers and scholars have paid little attention to these issues. In this chapter, preliminary Swedish findings from a European comparative study on 0- to 3-year-olds and their digital life are presented and discussed in relation to domestication and parental mediation of media.