Abstract: Sparse decomposition algorithm is one of the hottest research topic in signal processing field and plays an important role in sparse representation and Compressive Sensing (CS) .Recently, beside sparsity, the structures that describes the dependencies of sparse coefficients has been exploited to improve the accuracy of sparse decomposition algorithms. It is called structured sparse decomposition algorithms. This paper will review the sparse signal model and structured sparse signal model. After that, two sparse decomposition algorithms based on Bayesian framework are introduced and their extensions to structured sparse signals are addressed. At last, the applications of structured sparsity in medical signal processing and audio signal processing are respectively demonstrated.