For the design of light-metal-sulfur batteries and for the understanding of their performance, knowledge on the stable crystalline polysulfides is very important. We confronted experimental and ab initio crystal structure prediction studies on the stability of Na polysulfides. The selected evolutionary-based structure-prediction algorithm was able to quickly and correctly predict the thermodynamically stable crystalline forms of Na polysulfides with small unit cells. For Na polysulfides with large unit cells, the algorithm correctly proposed short unbranched polysulfide chains to be energetically favorite structural motifs, but could not find proper three-dimensional structures in the limited number of generations. Experimentally, the polysulfides were studied by X-ray diffraction and 23 Na solid-state NMR spectroscopy. Complemented by calculations of the isotropic chemical shifts and quadrupolar coupling constants, NMR spectroscopy proved to be an excellent tool for the examination of Na polysulfides, because it allowed easy distinction and quantification of components in the samples.