Abstract: Two-grid algorithm of miscible displacement problem is reviewed. Firstly, the characteristic finite element method, the characteristic mixed finite element method and the characteristic expansion mixed finite element two-grid algorithm for the incompressible miscible displacement problem are presented. Then, the characteristic finite element two-grid algorithm for the compressible miscible displacement problem is discussed. Numerical examples are given to illustrate the effectiveness of the two-grid algorithm. Finally, the direction of further research on the two-grid algorithm for miscible displacement problem is discussed.