  We study a periodic medium driven over a random or periodic substrate. Our
work is based on nonequilibrium continuum hydrodynamic equations of motion,
which we derive microscopically. We argue that in the random case instabilities
will always destroy the LRO of the lattice. In most, if not all, cases, the
stable driven ordered state is a transverse smectic, with ordering wavevector
perpendicular to the velocity. It consists of a periodic array of flowing
liquid channels, with transverse displacements and density (``permeation
mode'') as hydrodynamic variables. We present dynamic functional
renormalization group calculations in two and three dimensions for an
approximate model of the smectic. The finite temperature behavior is much less
glassy than in equilibrium, owing to a disorder-driven effective ``heating''
(allowed by the absence of the fluctuation-dissipation theorem). This, in
conjunction with the permeation mode, leads to a fundamentally analytic
transverse response for $T>0$. Our results are compared to recent experiments
and other theoretical work.
