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The study of deforming continuous media is a well developed branch of solid mechanics which relies on models that assume displacements within the media are sufficiently smooth such that they can be modeled with partial differential equations.However, observations of nature show that some displacements exist where the spacial partial derivatives cannot be evaluated,most notably at the tip of a moving crack.The peridynamic theory of solid mechanics (peridynamics) utilizes models that do not require the existence of spacial derivatives and seeks to unify the mechanics of continuous and discontinuous media.Peridynamics has been shown to be useful in the modeling of material failure due to fracture, without the need redefine the media of interest to exclude the cracks.It is also showing promise in coupling of other types discontinuous media (i.e.particles, atoms) to continuum bodies using a consistent mathematical framework.This seminar will introduce the audience to the peridynamic theory, including discussion of the non-local length scale, constitutive modeling, computational methods, and interesting examples with special application to dynamic fracture, fragmentation, and penetration mechanics.