Many algorithms have been proposed to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories:greedy pursuit algorithms,lp norm regularization based algorithms,and iterative shrinkage algorithms. We summarize their pros and cons as well as their connections. Based on recent evidence,we conclude that the algorithms of the three categories share the same root:lp norm regularized inverse problem. Finally,several topics that deserve further investigation are also discussed. Many papers have an been found to find sparse representations over redundant dictionaries or transforms. This paper gives an overview of these algorithms by classifying them into three categories: greedy pursuit algorithms, lp norm regularization based algorithms, and iterative shrinkage algorithms. We summarize their pros and Based on recent evidence, we conclude that the algorithms of the three categories share the same root: lp norm regularized inverse problem. Finally, several topics that deserve further investigation are also discussed.