  We investigate the depinning transition occurring in dislocation assemblies.
In particular, we consider the cases of regularly spaced pileups and low angle
grain boundaries interacting with a disordered stress landscape provided by
solute atoms, or by other immobile dislocations present in non-active slip
systems. Using linear elasticity, we compute the stress originated by small
deformations of these assemblies and the corresponding energy cost in two and
three dimensions. Contrary to the case of isolated dislocation lines, which are
usually approximated as elastic strings with an effective line tension, the
deformations of a dislocation assembly cannot be described by local elastic
interactions with a constant tension or stiffness. A nonlocal elastic kernel
results as a consequence of long range interactions between dislocations. In
light of this result, we revise statistical depinning theories and find novel
results for Zener pinning in grain growth. Finally, we discuss the scaling
properties of the dynamics of dislocation assemblies and compare theoretical
results with numerical simulations.
