Since Huynen's original work, there have been many other proposed target decomposition theorems. In this paper, we provide a review of the different approaches used for target decomposition theory in radar polarimetry and classify three main types of theorems: those based on Mueller matrix, those using an eigenvector analysis of the coherency matrix, and those employing coherent decomposition of the scattering matrix. Support vector machine (SVM), as a novel approach in pattern recognition, has demonstrated a success in many fields. Here we first extract scattering mechanisms of radar targets by target decomposition and color composite. Then we propose a new algorithm of target classification by combining target decomposition and support vector machine. We conduct the experiment on the polarimetric synthetic aperture radar data. Experimental results show that: it is feasible and efficient to target classification by designing SVM classifiers using target decomposition, and the effects of kernel functions and its parameters on the classification efficiency are significant.