Abstract
The continuum theory of dislocation fields is discussed in this chapter with an emphasis on the formulations relevant to infinitesimal deformation of single crystals. Both the classical and contemporary developments are concisely outlined. The classical theory of dislocation fields is introduced first for static and dynamic dislocation configurations, followed by a brief discussion of the shortcomings of the classical theory in predicting plasticity of crystals. In this regard, the lack of connection between the evolution of the dislocation field and internal stress state of the crystal is particularly highlighted. The more recent phenomenological and statistically-based formalisms of continuum dislocation dynamics are then introduced. As discussed in the pertinent sections, these formalisms properly connect the evolution of the dislocation fields with the internal stress state in and thus offer frameworks for predicting the plastic behavior of crystals.