The acoustic emission (AE) technique is suitable for monitoring and evaluating hydraulic concrete damage due to its good response to material damage. While continuously advancing conventional AE analysis methods, various advanced digital processing technologies and intelligent algorithms have been applied to deeply explore the damage information and evaluate hydraulic concrete damage. An intelligent framework for evaluating hydraulic concrete damage based on AE has been established, according to the working principle of the AE monitoring system for hydraulic concrete damage. Based on the content involved in this framework, a review is conducted on the current research status of hot topics such as conventional analysis methods, signal processing methods, acoustic source localization (ASL) methods, AE source recognition methods, and deep learning technique applications. The complex characteristics of AE signals of hydraulic concrete damage and the research needs of how to overcome the adverse effects have been summarized, aiming to continuously improve the framework and achieve the construction of an intelligent platform for evaluating hydraulic concrete damage based on AE.