This chapter focuses on solving the problem of group sparsity. It studies the group-sparse synthesis prior recovery problems and discusses solution to analysis prior problems. The chapter illustrates how to solve an equality-constrained group-sparsity recovery problem. The analysis prior formulation assumes that the signal is not sparse but has a sparse representation in another basis (or transform). Unlike the synthesis prior formulation, it recovers the signal itself rather than the transform coefficients. The chapter discusses block orthogonal matching pursuit (BOMP) algorithm, group orthogonal matching pursuit (GOMP) algorithm, block matching pursuit algorithm, stagewise BOMP, and stagewise weak GOMP algorithm.