In view of the considerable progress that has been made over the last 40 years on the microstructural design of silicon nitride and related materials of tailored properties for specific applications, a clear review of the current understanding of the crystal structure and crystal chemistry of silicon nitride is timely. The crystal structures, crystal chemistry, and lattice defect nature of silicon nitride are critically reviewed and discussed, with emphasis placed firstly on the structural nature of alpha-silicon nitride (whether it is a pure silicon nitride, or should better be regarded as an oxynitride); and secondly on the space group of beta-silicon nitride (whether it is P6(3)/m or P6(3)). In conjunction with recent observations of vacancy clusters in alpha-silicon nitride, a comprehensive view compatible with all the experimental facts with respect to the structural nature of alpha-silicon nitride is tentatively presented.