Dislocations are line defects in crystals and they are considered the main mechanism of plastic deformations in metals. We will consider straight dislocations, so that their positions are completely identified by the intersections of the dislocation line with an orthogonal plane. In this talk we will present a purely variational approach, based on Gamma-convergence, to the study of the asymptotic behavior of the static energy induced by a finite system of dislocations as the atomic scale goes to zero. For a special class of dislocations, the so-called screw dislocations, we derive also an interaction between the defects, which drives their dynamics. The essential tool in all the results we will present is given by the analogy between dislocations and vortices in superconductors, studied within the Ginzburg-Landau framework. The results are obtained in collaboration with R. Alicandro, A. Garroni and M. Ponsiglione.