Numerical methods that conserve at least some of structural properties of systems are called geometric integrators or structure-preserving algorithms. Examples of such structural properties include symplectic structure, phase space volume, first integrals, symmetries, and so on. In the numerical analysis of differential equations, geometric integrators play an important role for the development and enhancement of practical discretization methods. Nowadays, it has been a criterion to judge the success of the numerical simulation. In this talk, I will introduce the concept of preserving-structure algorithms and some applications for many partial differential equations.