Beyond the standard lore of the SZ effect

The recent 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 leptonic 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.