With the breakout of the big data era, the data we are interested in is more and more complex. Especially, the model with matrix coefficient is in urgent to be constructed and solved. Many scholars are devoted to studying the statistical property analysis and designing algorithms for solving the matrix model. When the random errors have expectation 0 and the same variance, the method based on the least square loss function may perform well. However, when the random errors are heteroscedastic or the distribution of the errors are heavy-tailed (such as bi-exponential distribution, t-distribution, etc.) or the data contain outliers, the robust methods should be considered. The common robust methods are LAD, Quantile, Huber, etc. Most of the current research on the robust methods focus on the linear regression problem. There is few research on matrix regression problem. In this paper, we start with the least squares models, then summarize and comment on some matrix regression models. At the same time, we list some papers and briefly introduce some of our recent work. Finally, for the robust matrix regression problem, we propose some ideas and prospects.