The acquisition of information on fish stress has been recognized as an urgent need for monitoring water quality, preventing disease, and improving welfare. Minimizing the potential stress-related impact on fish health has attracted public attention by effectively and reliably identifying early signs of stress response in intensive aquaculture. To date, fish stress has been mainly monitored, identified, and evaluated manually, which is time-consuming, laborious, insufficient, and unreliable. Recently, intelligent methods and equipment create new opportunities for the automatic recognition of abnormal states involving behavioral and physiological stress responses of fish. This study reviewed the relevant articles on fish stress monitoring and summarized that the novel technologies were sorted into three categories: machine vision-based, sensor-based, and acoustic-based methods. All methods were assessed for their applications, advantages, and disadvantages, respectively. It is concluded that advanced sensors and machine learning-based methods are essential for accelerating the automation and intelligence of fish welfare monitoring technology. This paper proposes that the information fusion and deep learning algorithms have the potential to further improve the accuracy of future research on abnormal behavior recognition in smart fish farming.