The tensions between tendencies to support and reject that can be observed in reception measures for newly-arrived students in Sweden are a consequence both of the general climate of hostility towards immigration in Europe, and features particular to Sweden. The paper summarises the historical background to the present situation, from the 1960s onwards, and points to some of the impacts for teachers and for civil society. The analysis will above all focus on three diverging but parallell trends and which overlap: dynamics of integration, dynamics of competition and social segregation; dynamics of 'securitisation'. These dynamics evolve within different conceptualisations of education, but also relate to social developments and conflicting visions for society as a whole.