This chapter deals with the recently re-emerged concept of computational thinking (CT) and its reception in mathematics education research and mathematics curriculum policy. We provide an overview of CT’s claimed potentials for mathematics teaching and learning and outline the most widely used definitions of CT in mathematics education research. Based on three illustrative cases from Denmark, Sweden, and England, we develop three typologies of ways in which CT and mathematics are related to each other in curricular resources. We also describe the opportunities and challenges these typologies are associated with for teachers in relation to connecting CT and mathematics in the mathematics education classrooms. We conclude the paper by discussing the relation between tendencies in how CT is enacted in mathematics curriculum policy and how it is studied in the mathematics education research community. Moreover, we reflect on the implications of this relation for the opportunities of informing CT in mathematics education through state-of-the-art research.