This chapter provides a discussion on greedy algorithms. It presents oracle, practical, and intuitive solutions for an under-determined linear inverse problem. The chapter discusses stagewise orthogonal matching pursuit that uses iterations in solving the linear inverse problem. Another algorithm that has enjoyed a lot of success in sparse signal recovery is the CoSamp. The algorithm is simple to implement, but the logic behind its success is mathematically involved. The chapter also describes the gradient pursuit techniques to address computational issues in orthogonal matching pursuit.