Abstract: The dam-break problem is important in the design and management of hydraulic engineering,which has always been studied. This paper reviews and summarizes the progress in this field as follows:the mathematical model and the difficulty of the analytical solutions is introduced;discusses the latest progress of the numerical solutions is discussed;the finite difference method,the Godunov method,the Boltzmann method,and the KFVS method of one-dimensional dam-break problem are introduced;the TVD method,the discontinuous finite element method,the finite volume method and characteristic method of two-dimensional dam-break problem are discussed;the applicability,the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.Meanwhile,According to the shortage at present and the need of the engineering field,the research direction and the developmental trend are proposed.