Hyperspectral imagery has a lot of applications in the national defense and civil fields.Especially, the anomaly target detection does not need any prior information and thus has become one of the key technologies and research hotspots in hyperspectral image processing and information extraction.Through systematic research and analysis, this paper summarizes the existing anomaly target detection algorithms in detail, analyzes and evaluates the key problems involved in anomaly target detection, gives the future development direction of the technology, such as sparse representation,tensor decomposition, and deep learning etc., and presents the existing problems of the algorithms.Some innovative ideas and future research trends are also proposed.