I
will discuss space-time symmetries of the motion of
particles in one-dimensional periodic potentials
under the influence of ac driving. Mastering these symmetries allows
to systematically violate them by a proper choice of the ac driving,
and thus to generate a nonzero directed current.
I will show generalizations of that concept to interacting particles,
quasiperiodic driving, and higher spatial dimensions.
I will present results for the classical and quantum cases.