  We investigate the microscopic mechanisms giving rise to plastic depinning
and irreversible flow in vortex matter. The topology of the vortex array
crucially determines the flow response of this system. To illustrate this
claim, two limiting cases are considered: weak and strong pinning interactions.
In the first case disorder is strong enough to introduce plastic effects in the
vortex lattice. Diffraction patterns unveil polycrystalline lattice topology
with dislocations and grain boundaries determining the electromagnetic response
of the system. Filamentary flow is found to arise as a consequence of
dislocation dynamics. We analize the stability of vortex lattices against the
formation of grain boundaries, as well as the steady state dynamics for
currents approaching the depinning critical current from above, when vortex
motion is mainly localized at the grain boundaries. On the contrary, a
dislocation description proves no longer adequate in the second limiting case
examined. For strong pinning interactions, the vortex array appears completely
amorphous and no remnant of the Abrikosov lattice order is left. Here we obtain
the critical current as a function of impurity density, its scaling properties,
and characterize the steady state dynamics above depinning. The plastic
depinning observed in the amorphous phase is tightly connected with the
emergence of channel-like flow. Our results suggest the possibility of
establishing a clear distinction between two topologically disordered vortex
phases: the vortex polycrystal and the amorphous vortex matter.
