  Multi-frequency (X-ray, optical and radio) observations of galaxy clusters
indicate that the atmospheres of these cosmic structures consist of a complex
structure of thermal (hot and warm) and non-thermal (with different origin and
spectra) distribution of electrons (and protons) which is, therefore, far from
its modelling as a single, thermal electronic gas. This evidence requires to go
beyond the simple, standard lore of the SZ effect. This task is challenging for
both the theoretical aspects of their modelling and for the experimental goals
to be achieved, but it will return a large amount of physical information by
using the SZ effect as a unique tool for astro-particle and cosmology.
