In this talk, we present the fundamentals of deformation microstructures in crystalline solids in microscopic scale. In this scale, the irregularities in the crystal structure are called dislocatons and under certain circumstances, they can evolve in their respective slip planes.It is believed that proper understanding of dislocations effects is the key to understanding the crystal plasticity. Such motion can be approximated by evolution of curves driven by the curvature and external forces. In the talk we focus on several key fundamental mechanisms of the dynamics of discrete dislocation curves in our model and also on the mathematical and the numerical modeling point of view.