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DL creates both new opportunities and a series of challenges for information and data processing in smart fish farming. This paper focuses on applications of DL in aquaculture, including live fish identification, species classification, behavioural analysis, feeding decisions, size or biomass estimation, and water quality prediction. The technical details of DL methods applied to smart fish farming are also analysed, including data, algorithms and performance. The review results show that the most significant contribution of DL is its ability to automatically extract features. However, challenges still exist; DL is still in a weak artificial intelligence stage and requires large amounts of labelled data for training, which has become a bottleneck that restricts further DL applications in aquaculture. Nevertheless, DL still offers breakthroughs for addressing complex data in aquaculture. 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