The best way of organizing creativity within organizations remains somewhat enigmatic to scholars, particularly when it comes to the role of constraints. On the one hand, creative organizations are often associated with freedom, autonomy, weak rules and few boundaries. On the other hand, several studies suggest that constraints, particularly design constraints, often stimulate creativity rather than suppress it. All in all, findings are mixed and inconclusive, and further research that explores this area of tension is required. The goal of this paper is twofold. Firstly, we introduce the topic of constraints and creativity, and raise some of the open questions in this field. By way of illustration, we report on a preliminary study about the role of constraints. Secondly, we set the stage for the contributions in this special issue on creativity and innovation under constraints, by identifying four central themes for further research. We subsequently outline the articles in this issue, and show how each of them contributes to one or more of these themes.