The management of urban stormwater has become increasingly complex over recent decades. Consequently, terminology describing the principles and practices of urban drainage has become increasingly diverse, increasing the potential for confusion and miscommunication. This paper documents the history, scope, application and underlying principles of terms used in urban drainage and provides recommendations for clear communication of these principles. Terminology evolves locally and thus has an important role in establishing awareness and credibility of new approaches and contains nuanced understandings of the principles that are applied locally to address specific problems. Despite the understandable desire to have a ‘uniform set of terminology’, such a concept is flawed, ignoring the fact that terms reflect locally shared understanding. The local development of terminology thus has an important role in advancing the profession, but authors should facilitate communication between disciplines and between regions of the world, by being explicit and accurate in their application.

Model predictive control (MPC) can be used to manage combined urban drainage systems more efficiently for protection of human health and the environment, but examples of operational implementations are rare. This paper reviews more than 30 years of partly heterogeneous research on the topic. We propose a terminology for MPC of urban drainage systems and a hierarchical categorization where we emphasize four overall components: the “receding horizon principle”, the “optimization model”, the “optimization solver”, and the “internal MPC model”. Most of the reported optimization models share the trait of a multiobjective optimization based on a conceptual internal MPC model. However, there is a large variety of both convex and non-linear optimization models and optimization solvers as well as constructions of the internal MPC model. Furthermore, literature disagrees about the optimal length of the components in the receding horizon principle. The large number of MPC formulations and evaluation approaches makes it problematic to compare different MPC methods. This review highlights methods, challenges, and research gaps in order to make MPC of urban drainage systems accessible for researchers and practitioners from different disciplines. This will pave the way for shared understanding and further development within the field, and eventually lead to more operational implementations.