Tensor decomposition is a significant method to deal with large-scale data, which can reduce the data effectively. The high-order tensor is widely used in neuroscience, signal processing, image analysis, computer vi- sion and other fields as it has such advantages as uniqueness, robustness to noises and zero impact on the origi- nal data of the spatial structure and internal potential information. In this paper, the traditional dimensionality reduction methods were introduced firstly, and their problems and shortcomings were also discussed. Secondly, general analysis of three classical algorithms of tensor decomposition was carried out from the aspects of algo- rithm, basic ideas, algorithm framework and algorithm applications of CP decomposition, Tucker decomposition and non-negative tensor decomposition. Then, The CP decomposition algorithm and the Tucker decomposition algorithm were compared and analyzed from different angles. Finally, the present situation, practical application and future research trends of tensor decomposition were summarized and analyzed.