Relevant advances in the knowledge of the water dynamics at mesoscopic scales are reviewed, while mainly focusing on the contribution provided by high resolution inelastic X-ray scattering (IXS). In particular it is discussed how the use of IXS has improved our understanding of viscoelastic properties of water at THz frequencies. This specifically involves some solid-like features such as the onset of shear wave propagation, a sound velocity surprisingly similar to the one of ice, and an anomalously low sound absorption coefficient. All these properties can be explained by assuming the coupling of THz density fluctuations with a structural relaxation process connected to the breaking and forming of hydrogen bonds (HBs). This review also includes more recent IXS results demonstrating that, upon approaching supercritical conditions, relaxation phenomena in water gradually lose their structural character becoming essentially collisional in character. Furthermore, GHz spectroscopy results on supercooled water, suggesting the occurrence of a structural arrest, are discussed. An overview of the new opportunities offered by next generation IXS spectrometers finally concludes this review.

More than two decades of inelastic X-ray scattering (IXS) studies on noble gases and alkali metals are reviewed to illustrate the advances they prompted in our understanding of the terahertz dynamics of simplest systems. The various literature results outline a remarkably coherent picture of common and distinctive behaviours of liquids and their crystalline counterparts. Furthermore, they draw a consistent and comprehensive picture of the evolution of collective modes at the crossover between the hydrodynamic and the single particle regime, their coupling with fast (sub-ps) relaxation processes and their gradual disappearance upon approaching microscopic scales. The gradual transition of the spectrum towards the single particle limit along with its coupling with collisional relaxations will be discussed in some detail. Finally, less understood emerging topics will be discussed as the occurrence of polyamorphic crossovers, the onset of non-hydrodynamic modes and quantum effects on the spectrum, as well as recent IXS results challenging our vision of the supercritical phase as an intrinsically homogeneous thermodynamic domain.

We report on small-angle x-ray scattering measurements on liquid water aimed at characterizing the pressure evolution of its large-scale structure. Diffraction profiles have been fitted assuming a Lorentzian dependence on the exchanged momentum. As a result, we observe an anomalous behavior of the diffracted intensity that tends to disappear, increasing either the pressure or the temperature. This effect is discussed in detail and imputed to the ability of hydrostatic pressure to weaken hydrogen bonds.

Nearly two decades of thorough inelastic X-ray scattering (IXS) studies of transverse-like excitation in the spectrum of simple amorphous materials are reviewed. Particular attention is given to the case of liquid water and other prototypical samples, through discussion of both solved and still open issues. The perspectives opened up by the development of next generation IXS instruments with unprecedented contrast and resolution bandwidth are briefly illustrated.