With the rapid development of modern remote sensing techniques, remote sensing image change detection has become one of the most important means of the land-cover monitoring process. It has been widely used in application areas such as Geographic Situation Detection, Land Survey, Ecosystem Monitoring, Disaster Monitoring and Assessment, Food Security Insurance and military reconnaissance. The fine spectral resolution of the hyperspectral (HS) image and the detailed spectral change information of the multitemporal HS images brings the possibility for detecting the subtle changes associated with the dynamic land-cover transition. However, the high complexity data structure, high dimensional data features, and high redundancy information of the HS images makes HS change detection extremely challenging. This paper reviews the research advance of multitemporal HS image change detection, including: (1) Traditional HS image change detection approach based on the generalized similarity measurement of the HS images, which mainly follows the modeling process of multispectral change detection methods; (2) Dimensionality reduction based HS image change detection approaches, which are designed to overcome the adverse effects of the high dimensionality, high redundancy properties of the HS images; (3) Statistical modeling based HS image change detection approaches, which determines the change detection results by modeling of the statistical properties and multi-dimensional correlations of the HS images; (4) Classification based HS image change detection approaches, which introduces the image classification strategy into the change detection process to provide guarantee for obtaining the “from-to” type change information; (5) Unmixing based HS image change detection approaches, which are mainly developed to solve the mixed pixel phenomenon caused by the low spatial resolution of HS images; (6) Deep learning based HS image change detection approaches, which applied the deep learning methods into the HS image change detection tasks. Finally, the three major challenges and future development of HS image change detection are prospected.