  We examine the dynamics of an elastic string interacting with quenched
disorder driven perpendicular and parallel to the string. We show that the
string is the most disordered at the depinning transition but with increasing
drive partial ordering is regained. For low drives the noise power is high and
we observe a 1/f^2 noise signature crossing over to a white noise character
with low power at higher drives. For the parallel driven moving string there is
a finite transverse critical depinning force with the depinning transition
occuring by the formation of running kinks.
