  We discuss the role of dislocation assemblies such as grain boundaries in the
dynamic response of a driven vortex lattice. We simulate the depinning of a
field-cooled vortex polycrystal and observe a general enhancement of the
critical current as well as a distinct crossover in the characterisitic of this
quantity as a function of pinning density. The results agree with analytical
predictions for grain boundary depinning. The dynamics of grain boundaries thus
proves an essential mechanism underlying the flow response of defected vortex
lattices and the corresponding transport properties of the superconducting
material. We emphasize the connection between the topological rearrangements of
the lattice and its threshold dynamics. Our theory encompasses a variety of
experimental observations in vortex matter as well as in colloidal crystals.
