This study investigates the role played by parents as mediators of young children's access and engagement with digital technologies. In Belgium, Germany, Latvia and Portugal, qualitative in-depth interviews were conducted with 10 families in each country, including one child between 6 and 7 years old. Our findings show that parents of young children mainly play the role of 'gatekeepers' when it comes to facilitating and constraining access to and use of digital technologies. Parents' perceptions of the efficacy of digital technologies as responsible entertainment and as educational tools influence the technologies available at home and accessible to the child. These perceptions in turn impact parents' mediation strategies with regard to children's actual use of digital technologies, with restrictive mediation -- of time and less of content -- and supervision applied most. The power exerted by parents over access and use may be understood as a limitation of the children's rights. On the other hand, parents are not always concerned with the right of protection as they believe -- sometimes incorrectly -- that they are in control of the content their children are exposed to.