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Fusion engines are fundamental components of multimodal interactive systems, to interpret temporal combinations of deterministic as well as non-deterministic inputs whose meaning can vary according to the context, user and task. While various surveys have already been released on the topic of multimodal interactive systems, the current paper focuses on the design, specification, construction and evaluation of fusion engines. The article first introduces the adopted terminology and the major challenges that fusion engines propose to solve. Further, a history of the work achieved in the field of fusion engines is presented according to the main phases of the BRETAM model. A classification of existing approaches for fusion engines is then presented. The classification dimensions include the types of applications, the fusion principles and the temporal aspects. Finally, unsolved challenges, such as software frameworks, quantitative evaluation, machine learning and adaptation, sketch future work in the field of fusion engines.