Constraints play a vital role as both restrainers and enablers in innovation processes by governing what the creative agent/s can and cannot do, and what the output can and cannot be. Notions of constraints are common in creativity research, but current contributions are highly dispersed due to no overall conceptual framing or shared terminology. This lack of unity hinders overt opportunities for cross-disciplinary interchange. We argue that an improved understanding of constraints in creativity holds a promising potential for advancements in creativity research across domains and disciplines. Here, we give an overview of the growing, but incohesive body of research into creativity and constraints, which leads us to introduce ‘creativity constraints’ as a unifying concept to help bridge these disjoint contributions to facilitate cross- disciplinary interchange. Finally, we suggest key topics and sub-concepts, including ‘late’, ‘self-imposed’, and ‘continua of creativity constraints’, to inform future cross-disciplinary work on creativity constraints.