Digital games are becoming more and more popular worldwide, arousing children’s interest and fostering their motivation. Furthermore, tablets and smartphones are increasingly popular and widespread all around the globe, guaranteeing access to the web and to an ever-growing availability of games. This paper is based on the assumption that introducing digital game play into primary schools may support the development and consolidation of some transversal skills in a way that is perceived by students as interesting and motivating. When the games are carefully selected, the great effort spent by children in playing will provide them with the possibility to acquire and exercise, at an early age, basic skills which are important for their future. In particular, in this paper, different modalities in which digital games can be used in primary schools to foster basic transversal skills are presented. Logic and spatial reasoning skills as well as computational thinking are in particular considered. The reported experiments show that game based activities, when appropriately organized, can positively affect students’ school performance as well as students’ learning attitudes and behavior.