The use of the Internet by children at an increasingly early age today constitutes a major challenge for families and schools, as well as affecting educational and social policy. This is a qualitative piece of research that analyzes parents' beliefs, everyday practices and the difficulties they face in teaching their children the benefits and risks inherent in Internet use. The researchers used the discussion group technique, with four groups of parents of primary school children from four different schools. The results indicate that they share a pessimistic rather than an optimistic attitude towards Internet use among children in this age group, and perceive a number of difficulties when trying to foster children's responsible use of Internet. A wide range of parental control and mediation strategies were identified (laying down rules, organization of time and space for Internet use, limits and supervision (direct, agreed-upon, non agreed-upon and technical), along with various support strategies (parent and sibling modeling, diverse teaching strategies for stimulation and family communication) which, with the exception of technical supervision, they often use to educate their children and control their behavior in other areas, and which form part of their general parenting style. The conclusions point to the need to develop digital competence among parents, and there is some justification for educational intervention such as in promoting collaboration between families and schools.