Peridynamics is a generalization of the standard theory of continuum mechanics that is compatible with the treatment of evolving discontinuities, especially cracks. It treats crack growth on the same mathematical basis as any other form of deformation, so it offers the possibility of modeling fracture without the need for special techniques. Its basic mathematical relations are integro-differential equations, rather than partial differential equations. Since its introduction over twenty years ago, the peridynamic theory has found numerous and diverse applications. Its numerical implementation is available in software such as LS-DYNA as well as more specialized meshless codes. This talk will describe the basic principles of the theory and offer a perspective on what has been learned about its strengths and weaknesses. The talk will also include examples of applications drawn from industry and defense. These include fatigue and fracture, erosion and wear, shock waves and their effects, fragmentation, impact and penetration, and coupling with multiple physical fields.