Matrix optimization problems (MOPs) have been recognized in recent years to be a powerful tool to model many important applications arising from emerging fields such as data science  {within and beyond the optimization community}. Perturbation analysis of optimization problems play a fundamental and crucial role in optimization, which provided important theoretical foundation for algorithm designing and others. Science MOPs are non-polyhedral, the corresponding analysis is totally different from that of the classical polyhedral case (e.g., the nonlinear programming). Basing on results obtained in [1,2], we summary the recent progress on perturbation analysis of MOPs.