Stereo matching is a fundamental and crucial problem in computer vision. In the last decades, many researchers have been working on it and made great progress. Generally stereo algorithms can be classified into local methods and global methods. In this paper, the challenges of stereo matching are first introduced, and then we focus on local approaches which have simpler structures and higher efficiency than global ones. Local algorithms generally perform four steps： cost computation, cost aggregation, disparity computation and disparity refinement. Every step is deeply investigated, and most work focuses on cost aggregation. We studied most of the classical local methods and divide them into several classes. The classification well illustrates the development history of local stereo correspondence and shows the essence of local matching along with its important and difficult points. At the end we give the future development trend of local methods.