In this manuscript, we analyse the attitudes and practices of Estonian parents (N = 198) who allowed their 0-3-year olds to use smart devices. We aimed to discover if there was an interaction between parental use of smart technologies, parents' attitudes and the child's age that would predict young children's usage of smart devices. We also wanted to find out what kinds of devices are made available for 0-3-year olds, how frequently parents allow the child to use them, the activities children are engaged in on smart devices and which apps they use during their digital play. Parental mediation practices were also analysed. Our results provide evidence that parent screen time, parent attitudes and the child's age are all associated with touch screen use among infants and toddlers. Parents give three main reasons when rationalising their child's touch screen use, related to education, entertainment and behaviour regulation. Although parental mediation strategies are dependent on the age and gender of the child, the majority of parents combine different mediation strategies in order to fulfil their role as mediators of young children's digital play.