Scaling laws and emergent effects for plasticity in heterogeneous materials Abstract: We revisit models that describe the propagation of dislocations through random heterogeneous media. We derive a fully nonlinear model describing the evolution of a dislocation in the line tension approximation in a homogeneous medium with random obstacles. We investigate the pinning (the dislocation becomes stuck) and depinning behavior (the dislocation line swipes over a strictly positive mean area per time unit) of this model for dislocation glide. We show that our model obeys Taylor Scaling i.e. the critical pinning force scales like the square root of the concentration of obstacles. As the energy dissipation of dislocations is not purely viscous we need to extend the theory of viscosity solutions to treat partial differential inclusions arising while modeling dry friction kinetics. The analysis of the pinning behavior is based on explicit construction of sub and supersolutions and hence the existence of a comparison principle is fundamental for our study. Finally we explore numerical methods for a relaxed model of dislocation slip