Detailed critical analysis of publications devoted to QSPR of aqueous solubility is presented in the review with discussion of four types of aqueous solubility (three different thermodynamic solubilities with unknown solute structure, intrinsic solubility, solubility in physiological media at pH=7.4 and kinetic solubility), variety of molecular descriptors (from topological to quantum chemical), traditional statistical and machine learning methods as well as original QSPR models.