In the recent years, the method of discrete dislocation dynamics simulations has become popular in studying the plasticity of crystals at the microscale and small strain levels (~ 1%). Practical levels of crystal deformation encountered in experiments and in metal processing require the development of dislocation based theories of plasticity that captures all deformation mechanisms at a larger scale. The method of continuum dislocation dynamics is believed to meet this objective. The method casts the dislocations dynamics problem in the form of transport-reaction models for crystal dislocations after expressing them in terms of density fields. At this point, however, the method faces theoretical challenges, including modeling of the dislocation reactions, collective mobility, short range interaction effects, and accounting for the finite deformation kinematics in its mathematical formulation. These issues will be discussed in this presentation, along with theoretical and computational progress made within the Materials Theory Group at Purdue.