Computing is no longer considered a subject area only relevant for a narrow group of professionals, but rather as a vital part of general education that should be available to all children and youth. Since making changes to national curricula takes time, people are trying to find other ways of introducing children and youth to computing. In Sweden, several current initiatives by researchers and teachers aim at finding ways of working with computing within the current curriculum. In this paper we present case studies based on a selection of these initiatives from four major regions in Sweden and based on these case studies we present our ideas for how to move forward on introducing computational thinking on a larger scale in Swedish education.