The minimum sum of absolute errors MSAE regression is resistant to outliers and error distributions with long tails. It also provides a good starting solution for certain robust regression procedures. A number of efficient algorithms and computer codes have been developed for the MSAE regression. Computer programs have also been included in two major statistical packages. Small sample properties as well as asymptotic distributional results and inferential procedures for the MSAE estimator are now available. Our objective in this paper is to briefly summarize the current state-of-the-art for the MSAE regression.