The local structure of liquid water as a function of temperature remains a source of intense research. This structure is intimately linked to the dynamics of water molecules, which can be measured using Raman, dielectric and infrared spectroscopy. Spectral peaks are usually interpreted in terms of the motions of single molecules or small clusters. From classical molecular dynamics simulations we find that some peaks in water's librational and OH stretching bands correspond to dispersive optical phonon-like modes. We argue that on subpicosecond time scales these modes propagate through water's hydrogen bond network over distances of up to two nanometers. In the long wavelength limit these optical modes exhibit longitudinal-transverse splitting, indicating the presence of coherent long range dipole-dipole interactions, as in ice. These results indicate the dynamics of liquid water have more similarities to ice than previously thought. In the second part of my talk I will discuss new methods for ab-initio simulation we are developing which combine density functional theory with path integral molecular dynamics, allowing for the inexpensive inclusion of nuclear quantum effects.