abstract: In this talk, I will describe what are dislocations lines in crystals, and propose a model for their dynamics. This model is a coupled system between elasticity and an eikonal equation. In the case of a single dislocation line, we get a single non-local eikonal equation, and will present some partial results of existence and uniqueness. At very large scales, the dynamics of the dislocation line is well approximated by an anisotropic mean curvature motion. I will present a corresponding convergence result.