Abstract: The damage and destruction process of concrete under a shock and a penetration is virtually the process of a mechanical model transformed from a continuum to a discontinuity. The classic continuum mechanics starts with an assumption of a spatially continuous and differentiable displacement field and solve the problem with partial differential equations. It is difficult to compute or model the whole process of the material and structure when suffering damage. Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. The theory assumes that particles in a continuum interact with each other across a finite distance, formulates problems in terms of integral equations rather than partial differential equations. In this paper, we introduce the theoretical and numerical system of PD and its modeling method. We also introduce the numerical method of structures when subjected to impact loading. The result of the example clarifies the unique advantage of modeling damage accumulation and progressive failure of concrete based on Peridynamics Theory. Finally, some open problems and future research trends in PD are discussed.