Many of the elastic systems we have discussed may be driven by
various external fields. Forces are exterted by these fields, which,
in the absence of impurity pinning, would cause the systems to slide
at some non-zero velocity. This force is exerted in a CDW by an
electric field, in a vortex system by a current, and on a
ferromagnetic domain wall by a magnetic field. At zero temperature,
with impurities, there can be a sharp depinning transition at
which the velocity of the system changes from v=0 (for 
) to
v > 0 (for 
). Such depinning phenomena are generally rounded
out at finite temperature, but if the temperature is low enough, the
effects of rounding may be quite small. One should then study the
zero temperature dynamics.
Zero temperature dynamics can be extremely rich, but it must also be realized that it is in many respects less universal than equilibrium behavior. I will distinguish three broad classes of such depinning phenomena, depending upon whether it is (a) purely elastic, (b) plastic with non-conserved density, or (c) plastic with a conserved density.