Abstract: SpMV (sparse matrix-vector multiplication) is a widely used kernel in scientific computing. Since the performance of specific SpMV program is closely related to the distribution of non-zero elements in sparse matrices, there is no universal SpMV program design that can achieve high performance in all matrices. Therefore, auto-tuning has become a popular method for high SpMV performance. This paper analyzes the difficulties in optimizing SpMV and introduces two representative works of auto-tuning: SMAT, which is based on pre-implemented templates and AlphaSparse which designs SpMV programs from scratch. This paper introduces their designs, implementations, test results, advantages, and disadvantages. Finally, the trend of SpMV auto-tuning is analyzed and predicted.