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In aquaculture, accurate and automatic quantification of fish behaviour can provide useful data input for production management and decision-making. In recent years, with the focus on fish welfare, it has become urgent to study and use nondestructive quantitative methods of fish behaviour in aquaculture. In this paper, based on the literature of the past 30 years, nonintrusive and automatic quantitative methods for fish behaviour are analysed. Firstly, several important fish behaviours in aquaculture are listed, and the quantification of fish behaviour is summarized in four stages: detection, tracking, feature extraction and behaviour recognition. Then, nonintrusive methods of fish behaviour quantification, through machine vision, acoustics and sensors, and their advantages and disadvantages are also compared and discussed in detail. It is concluded that the combination of multiple methods and deep learning is a key technology for fish behaviour quantification, which has gradually become a popular focus of research and application in recent years. This review can be used as a reference to improve fish behaviour quantification in future, so as to create a more effective and economic technical method.