The problem of finding sparse solutions to underdetermined systems of linear equations arises in several real-world problems (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the l1-regularized least squares approach that has been recently attracting the attention of many researchers. In this talk, we focus on variable fixing and active set approaches. We describe two different methods and analyze their convergence properties. Finally, we report numerical results on some test problems showing the effectiveness of the approaches.