The properties of the NaxCoO2 class of materials are of interest from a number of viewpoints. These compounds are based on a triangular lattice of spin-½ ions—prototype RVB system— where a high thermoelectric-power Curie-Weiss metallic paramagnet is found for Na0.7CoO2, a charge ordered insulator at x=0.5, and a paramagnetic metal where superconductivity is induced in Na0.3CoO2 when it is intercalated with water. Here we briefly review our neutron diffraction and inelastic scattering measurements characterizing the crystal structure and lattice dynamics, and relate these to the observed physical properties. The basic structure of NaxCoO2 is hexagonal and consists of robust layers of CoO2 interspersed by Na layers with two inequivalent sites. Two special cases are x=1 where one of these sites is fully occupied and the other empty, and x=½ where both sites have equal occupancies of ¼ and the system is a charge ordered insulator. For general × the site occupancies are inequivalent and vary systematically with x. In the regime of x=0.75 we find a first-order transition from a high symmetry Na site at low T to a three-fold split site (with lower symmetry) at high T. This transition is first order and varies with x. For the Na0.3CoO2. 1.4(H/D)2O superconductor, the water forms two additional layers between the Na and CoO2, increasing the c -axis lattice parameter of the hexagonal P 63/mmc space group from 11.16 Å to 19.5 Å. The Na ions are found to occupy a different configuration from the parent compound, while the water forms a structure that replicates the structure of ice to a good approximation. We find a strong inverse correlation between the CoO2 layer thickness and the superconducting transition temperature (TC increases with decreasing thickness). The phonon density-of-states for Na0.3CoO2 exhibits distinct acoustic and optic bands, with a high-energy cutoff of ∼100 meV. The lattice dynamical scattering for the superconductor is dominated by the hydrogen modes, with librational and bending modes that are quite similar to ice, supporting the structural model that the water intercalates and forms ice-like layers in the superconductor.