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This paper aims to present a comprehensive survey on water quality soft-sensing of a wastewater treatment process (WWTP) based on artificial neural networks (ANNs). We mainly present problem formulation of water quality soft-sensing, common soft-sensing models, practical soft-sensing examples and discussion on the performance of soft-sensing models. In details, problem formulation includes characteristic analysis and modeling principle of water quality soft-sensing. The common soft-sensing models mainly include a back-propagation neural network, radial basis function neural network, fuzzy neural network (FNN), echo state network (ESN), growing deep belief network and deep belief network with event-triggered learning (DBN-EL). They are compared in terms of accuracy, efficiency and computational complexity with partial-least-square-regression DBN (PLSR-DBN), growing ESN, sparse deep belief …