Sound-driven gas bubbles in water can emit light pulses. This phenomenon is called sonoluminescence (SL). Two different phases of single bubble SL are known: diffusively stable and diffusively unstable SL. Phase diagrams are presented in the gas concentration versus forcing pressure state space and also in the ambient radius versus forcing pressure state space. These phase diagrams are based on the thresholds for energy focusing in the bubble and of (i) shape instabilities and (ii) diffusive instabilities. Stable SL only occurs in a tiny parameter window of a large forcing pressure amplitude P[inf a]~1.2--1.5 atm and a low gas concentration of less than 0.4% of the saturation. The upper concentration threshold becomes smaller with increasing forcing. The results quantitatively agree with experimental results of Putterman's UCLA group on argon, but not on air. However, air bubbles and other gas mixtures can also successfully be treated in this approach if, in addition, (iii) chemical instabilities are considered. The essential feature is the removal from the bubble of almost all the nitrogen and oxygen as reaction products (i.e., NO[inf x] or NH[inf 3]). Inert gases are crucial for stable sonoluminescence because they do not react with the fluid.