The Na-23 and Si-29 NMR spectra of the sodium-silicon clathrate materials Na8Si46 and NaxSi136 (1 < x < 24) and the parent Zintl phase NaSi have been studied in detail with a view to ironing out a number of ambiguities in the published literature and to determining properties of these potential thermoelectric materials. Sharp spectra are obtained only when the clathrate cages are close to fully occupied by Na, so that crystallographic symmetry is achieved. Signals from Na in the small and large cages of both structures have been unequivocally assigned. The pseudospherical cages give isotropic Na-23 lines, whereas the other cages produce first-order quadrupolar line shapes. Electric field gradients derived from these spectra, and ab initio calculations are in remarkable agreement. The large Knight shifts of both types of nuclei have rather unusual temperature dependences, which reflect the changing distributions of unpaired electron density in the conduction bands. As the Na content of NaxSi136 is reduced there is drastic broadening of the Na-23 and Si-29 spectra due to a random distribution of vacant cages and hence of environments, and the Si spectra shift to lower frequencies, indicating a reduction in conduction s-electron density on the Si. Intensity data suggest a preferential loss of Na from the large cages. XPS results show a protective coating of silica on the surface of the clathrates. NMR,XPS, and XANES results all indicate transfer of electrons from Na to the Si framework, as predicted by calculations. XANES shows a lowering of the absorption edge, and hence of the conduction band, of both clathrates relative to crystalline Si.