  In this article, we review different studies based on advanced x-ray
diffraction techniques - especially coherent x-ray diffraction - that allowed
us to reveal the behaviour of such symmetry-breaking systems as Charge Density
Wave (CDW) and Spin density Wave (SDW), through their local phase. After a
brief introduction on the added value of using coherent x-rays, we show how the
method can be applied to CDW and SDW systems, in both static and dynamical
regimes. The approach allowed us to probe the particular sliding state of CDWs
systems by observing them through their phase fluctuations, to which coherent
x-rays are particularly sensitive. Several compounds stabilizing a CDW phase
able to slide are presented, each with a different but clearly pronounced
signature of the sliding state. Two main features emerge from this series of
experiments which have been little treated until now, the influence of CDW
pinning by the sample surfaces and the propagation of periodic phase defects
such as charge solitons across the entire sample. Phase models describing the
spatial and temporal properties of sliding CDWs are presented in the last part
of this review.
