Classification is one of the core components in the interpretation of Polarimetric Synthetic Aperture Radar (PolSAR) images. A new PolSAR image classification approach employs the structural properties of the Riemannian manifold formed by PolSAR covariance matrices. In this paper, we first review the Riemannian manifold metrics generally used in PolSAR image analysis. Then, we describe a sparse coding method for the covariance matrices in the Riemannian manifold. For supervised classification, we propose a PolSAR image classification method that considers spatial information based on kernel space sparse coding. As for unsupervised PolSAR image classification, a method that takes advantage of Riemannian sparse induced similarity is proposed. Experimental results on EMISAR and AIRSAR data demonstrate the effectiveness of the proposed methods.