The computation of matrix exponential which ties up structural mechanics and optimum control is one of the extensive topics in numerical mathematics. ’Though there are many algorithms about the matrix exponential such as Pade-scaling and squaring-approximation (PSSA)，precise integration method (PIM)and some results about those optimal computational cost, it is far from satisfying to us. Currently Lie group methods are of huge value and they are popular abroad and lead to the computation of matrix exponential to be a hot topic. Since numerical approximation must run in Lie groups or Lie algebras, some classic methods are no effect. It is more difficult than classic method. In this paper a few popular computation methods of matrix exponential are reviewed systematically and evaluated in detaA and some problems which need our thorough research are put forward.