Inelastic X-ray Scattering (IXS) techniques have the potential for studying the dynamical properties of materials in great detail. Compton scattering provides information on the momentum distribution of the electrons and from this one can learn about coulombic and magnetic correlations in the electron gas. IXS with high-energy resolution gives direct access to the electronic structure, by allowing the direct determination of the energy and momentum-resolved dielectric function. When the energy resolution is pushed into the milli-electron volt regime, it also enables the determination of the atom dynamics at wavelengths comparable to the typical inter-particle distances. Moreover, resonant IXS from nuclei gives the possibility of determining the density of states (DOS) of the vibrational states in the investigated system (phonon DOS for crystalline materials). Each one of these challenging IXS methods received a tremendous impulse from the advent of third-generation synchrotron radiation sources. At the ESRF in particular, each has a state-of-the-art setup. Every year we observe the production of important new results in challenging scientific programs, as well as the demonstration of new potentials thanks to instrumental developments and to a better comprehension of the methods and of their domain of applications. 

In this chapter of the Highlights, we want to give a flavour of the typical problems studied on these beamlines. The small and intense beams provided at the ESRF give the possibility of studying matter under high pressure while making use of IXS techniques. Specifically on ID22N and on ID28, extended studies of iron under high pressure have allowed the investigation of the elastic properties of iron at pressures approaching those at the Earth's core, and the formulation of specific new hypotheses on the chemical composition of iron in the Earth. Similarly, on ID28, the phonon dispersion curves have been determined in GaN single crystals, which can be produced only in very small sizes. On ID18, the DOS of phonons in quasicrystals projected on the iron atoms have been successfully determined allowing a new understanding of the DOS obtained from neutron data. Another challenging area of application of IXS is the determination of the collective dynamics in disordered systems, and, in this growing field, very detailed studies are now possible on ID16 and ID28, as demonstrated by the observation of the onset of the localisation of the acoustic modes in liquid ammonia and by the analysis of Umkalpp-processes in a disordered system such as liquid lithium. Finally Compton spectroscopy and high-energy X-ray diffraction on ID15 has enabled the study of electron correlation effects in beryllium and the discovery of charge ordering in manganites and nickelates exhibiting the colossal magnetoresistance effect.

These highlights give a feeling for the high degree of maturity of the IXS methods, and on their capability to provide valuable information about the dynamical properties of electrons and atoms in a wide variety of materials exhibiting interesting behaviours from both a fundamental and an applied point of view.