This review article focuses on the most recent advances in X-ray and neutron scattering studies of water structure, from ambient temperature to the deeply supercooled and amorphous states, and of water diffusive and collective dynamics, in disparate thermodynamic conditions and environments. In particular, the ability to measure X-ray and neutron diffraction of water with unprecedented high accuracy in an extended range of momentum transfers has allowed the derivation of detailed O-O pair correlation functions. A panorama of the diffusive dynamics of water in a wide range of temperatures (from 400 K down to supercooled water) and pressures (from ambient up to multiple gigapascals) is presented. The recent results obtained by quasi-elastic neutron scattering under high pressure are compared with the existing data from nuclear magnetic resonance, dielectric and infrared measurements, and modeling. A detailed description of the vibrational dynamics of water as measured by inelastic neutron scattering is presented. The dependence of the water vibrational density of states on temperature and pressure, and in the presence of biological molecules, is discussed. Results about the collective dynamics of water and its dispersion curves as measured by coherent inelastic neutron scattering and inelastic X-ray scattering in different thermodynamic conditions are reported.