Abstract: The polarimetric SAR technology (PolSAR) has become essential method in earth observation research due to the advantages of all-time and all-weather. The full PolSAR system can obtain signals in four channels by transmitting and receiving radar waves with horizontal and vertical polarization, which improves the ability to describe different ground targets. The PolSAR decomposition can extract the geometric and physical properties recorded by observations and promote the development of PolSAR applications. It therefore has received extensive attention. In this study, starting from the principle of interaction between PolSAR signals and targets, systematically expounding the mainstream algorithms, which can be summarized into three categories, including coherent decomposition methods represented by Pauli, Krogager, and Cameron decompositions; and incoherent decomposition represented by Freeman-Durden, Cloude-pottier decompositions; and image visualization method represented by polarization characteristic map and polarization projection map. The principles of different methods are summarized, and the interpretation performances of different methods for forests, crops, orthogonal buildings, and oriented buildings under the observation of C, L, and P band SAR signals are compared. The advantage of the coherent decomposition is that it is simple and easy to understand, without involving complex second-order statistical operations. However, its limitation is that it cannot describe the scattering characteristics of distributed targets, which hinders the development of coherent target decomposition. The advantage of model-based decomposition lies in its clear physical meaning, which plays an important role in different applications. However, its main limitation is the coupling between scattering components and the coupling between structure, orientation, and dielectric constant, making it difficult to comprehensively understand the geometric physical properties of targets. Eigenvalue-based decomposition has a rigorous mathematical background and can avoid model coupling. However, this method can only identify three dominant scatterers within each resolution cell. In addition, due to the variation of eigenvectors, it increases the difficulty in understanding their physical meaning. Image visualization methods visualize the interaction process between PolSAR signals and targets, facilitating a fine exploration of scattering information. However, rich polarization information provided increases the difficulty in extracting geometric physical features of targets, limiting its application scope to object classification and similar applications. Furthermore, two key challenges faced by the interpretation of PolSAR image and potential ways to solve these two problems are introduced. The purpose of this paper is to deepen the understanding of the interaction process between PolSAR signals and ground targets and to promote the development of PolSAR applications.