Signatures of correlation: from excitons to satellites

One of the simplest, yet most striking, outcomes of electron correlation is the exciton. The creation of electron-hole pair(s), under external perturbation, is an intrinsic collective excitation of the system and, from the theoretical point of view, is defined in terms of beyond single-particle . In this contribution I will first illustrate the importance of excitonic effects in the optical spectrum of solids, taking Vanadium dioxide as an example, underlying some general (local fields, de-polarization effects) and technical aspects (starting point of perturbative approaches, self-consistency). In a second part, I will focus on the generality of the screening concepts, and the interchange among theoretical approaches: Bethe-Salpeter equation, Time Dependent Density Functional Theory, GW approximation) as well as spectroscopy techniques (optical, Inelastic X-ray scattering, Electron Energy Loss and Photo-emission spectroscopy).