  We consider the driven dynamics of Wigner crystals interacting with random
disorder. Using numerical simulations, we find a rich variety of transport
phenomena as a function of charge density, drive, and pinning strength. For
weak pinning, the system forms a defect free crystal that depins elastically.
When the pinning is stronger, a pinned glass phase appears that depins into a
filamentary flow state, transitions at higher drives into a disordered flow
phase, and finally forms a moving smectic. Within the filamentary flow phase,
the conduction curves can show switching dynamics as well as negative
differential conductivity in which switching events cause some flow channels to
be blocked. The velocity noise in the filamentary flow regime exhibits narrow
band characteristics due to the one-dimensional nature of the motion, while the
moving smectic has narrow band velocity noise with a washboard frequency. In
the disordered flow state, the noise power reaches a peak value and the noise
has a $1/f$ character. Our transport results are consistent with recent
experimental transport studies in systems where Wigner crystal states are
believed to be occurring. Below the conduction threshold, we find that
avalanches with a power law size distribution appear when there are sudden
local rearrangements of charges from one pinned configuration to another.
