  We study the depinning of a flux line by analytical and numerical methods
applied to a phenomenological equation of motion. Transverse fluctuations do
not influence the critical behavior of the longitudinal component, justifying
``planar approximations". In an isotropic medium, longitudinal fluctuations
have a roughness exponent $\zeta_\parallel=1$, and relax with a dynamic
exponent $z_\parallel\approx4/3$; transverse fluctuations are suppressed
($\zeta_\perp=1/2<\zeta_\parallel$), and relax more slowly, with
$z_\perp=z_\parallel+1$. Anisotropy in the depinning threshold, or
orientational dependence of force-force correlations, lead to new universality
classes.
