With the continuous development of information technology, the scale of time series data has grown exponentially, which provides opportunities and challenges for the development of time series anomaly detection algorithm, making the algorithm in this field gradually become a new research hotspot in the field of data analysis. However, the research in this area is still in the initial stage and the research work is not systematic. Therefore, by sorting out and analyzing the domestic and foreign literature, this paper divides the research content of multidimensional time series anomaly detection into three aspects: dimension reduction, time series pattern representation and anomaly pattern detection in logical order, and summarizes the mainstream algorithms to comprehensively show the current research status and characteristics of anomaly detection. On this basis, the research difficulties and trends of multi-dimensional time series anomaly detection algorithms were summarized in order to provide useful reference for related theory and application research.