The peridynamic theory of solid mechanics, developed at Sandia, is a nonlocal extension of classical continuum mechanics for discontinuities and long-range forces. It is a mathematical theory that unifies the mechanics of continuous media, cracks, and discrete particles. Our research in peridynamics span a number of interrelated areas, including mathematics, mechanics, constitutive-model development, scientific computing, and engineering. We apply peridynamics with a focus on pervasive material failure and fracture to meet the challenges of Sandia’s national security missions. Our work is enriched through ongoing collaborations with academia and industry.