This thesis concerns with Dynamic Discrete Dislocation Plasticity (D3P), a planar method of discrete dis- location dynamics aimed at the study of plastic relaxation processes in crystalline materials subjected to weak shock loading and high strain rates. Traditionally, the study of plasticity under these condi- tions was based on experimental measurement of the macroscopic response of the material. Using these data, well-known macroscopic constitutive laws and equations of state have been formulated. However, direct simulation of dislocations as the dynamic agents of plasticity in those circumstances remains a challenge. In discrete dislocation dynamics (DDD) methods, in particular planar discrete dislocation plasticity (DDP), dislocations are modelled as discrete discontinuities in an elastic contin- uum. Current DDP and DDD methods are unable to adequately simulate plastic relaxation because they treat dislocation motion quasistatically, neglecting the time-dependent nature of the elastic fields and assuming that they instantaneously acquire the shape and magnitude predicted by elastostatics. This thesis proves that under shock loading, this assumption leads to models that invariably break causality. This thesis posits that these limitations can only be overcome with a fully time-dependent formulation of the elastic fields of dislocations. A truly dynamic formulation for the creation, annihi- lation, and nonuniform motion of straight edge dislocations is derived, extending the DDP framework to a fully elastodynamic formulation, D3P. This thesis describes the changes in paradigm that D3P poses, including retardation effects in dislocation interactions and the effect of the dislocation past history. The thesis then builds an account of all the methodological aspects of D3P that have to be modified from DDP, including mobility laws, generation rules, etc. Finally, the thesis explores the ap- plications D3P has to the study of plasticity under shock loading. It is found that, D3P elastodynamic formulation is able to explain the attenuation of the dynamic yield stress in a shock as a cumulative interference of elastic waves.