  We review the physics of magnetic quantum oscillations in quasi-one
dimensional conductors with an open Fermi surface, in the presence of modulated
order. We emphasize the difference between situations where a modulation
couples states on the same side of the Fermi surface and a modulation couples
states on opposite sides of the Fermi surface. We also consider cases where
several modulations coexist, which may lead to a complex reorganization of the
Fermi surface. The interplay between nesting effects and magnetic breakdown is
discussed. The experimental situation is reviewed.
