Brønsted superbases have wide applications in organic chemistry due to their ability to activate C-H bonds. The strongest neutral bases to date are substituted aminophosphazenes developed in the late 1980s by Reinhard Schwesinger. Since then, much effort has been expended to create even stronger neutral bases. In this article, the reasons for the instability of very basic compounds are investigated by means of high-level quantum-chemical calculations. Theoretical basicity limits are suggested for solutions as well as for the gas phase. A record-breaking superbase most likely to be synthesizable and stable at ambient conditions is proposed. Hexamethylphosphoramide is considered a reliable ionizing solvent for superbases.