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In recent years, with the rapid development and expansion of the global aquaculture industry, and the continuous enlargement of aquaculture farms, the industrialization, intelligence, and informatization of aquaculture have become a trend in the industry. China has become the largest producer of fisheries and aquaculture. Fish farming is an important component of aquaculture, and fish farming monitoring has become an important technology to enhance the efficiency, production, and management of fish farming. Fish farming monitoring can provide real-time and accurate data for farms, assisting farm managers in making decisions to improve efficiency and production. With the emergence of artificial intelligence technology in recent years, deep learning has rapidly developed and been widely applied in various fields such as image and audio recognition, natural language processing, robotics, bioinformatics, chemistry, and finance. The monitoring of fish farming focuses on the quantity, growth, behavior, and health status of fish. Using deep learning technology, we can quickly and accurately obtain information related to fish farming and enhance its efficiency and management. This paper presents a deep learning-based method for fish farming monitoring and reviews the literature progress in fish length measurement, fish counting, fish feeding, fish swimming behavior, and fish disease diagnosis. Although deep learning-based fish length measurement has achieved high accuracy in underwater environments, some errors still exist. The counting methods based on deep learning can be categorized into segmentation counting, detection counting, tracking counting, and density regression counting. Deep learning models based on video data have higher accuracy in recognizing fish feeding behavior than imagebased models. There have been many studies on fish tracking, but practical applications still face challenges such as fish feature extraction, the influence of fish size and obstructions, and occlusion issues. In fish disease diagnosis, it is necessary to establish standardized and shared fish disease datasets and utilize data fusion, data level information fusion, feature level information fusion, and decision level information fusion. This article also summarizes the main problems of deep learning-based visual technologies in fish farming monitoring from the aspects of monitoring data acquisition and transmission, dataset standardization and processing, deep learning model design, and the lack of business application in fish farming intelligent monitoring. The problems in data acquisition include a limited variety of experimental subjects, a small number of samples, and poor performance of experimental equipment. In the data transmission process, there are challenges in data security and realtime transmission. In terms of datasets, there is a low level of standardization and a lack of large-scale unified datasets. There is also a lack of research on large models and embedded models in deep learning model design. Furthermore, there is a realistic problem of insufficient business application in practical settings. The paper also proposes future research directions, including establishing fish farming monitoring datasets, super-scale parameter models for fish farming, edge computing for terminal monitoring devices, and digital twinning in fish farming monitoring, aiming to provide scientific references for the widespread application of deep learning in fish farming monitoring. [ABSTRACT FROM AUTHOR]