Theoretical studies on the metal-aqueous electrolyte solution interface are critically reviewed with emphasis on the studies using quantum treatments for the metal side and classical approaches, above all, integral equation theories, for the solution side. With the integral equation theories an infinitely large system can be mimicked, and ions can readily be incorporated in the solvent at a finite concentration. The density structure of water molecules and ions, water and ion configurations near the metal surface, and the potential drop across the interface are discussed and some of them are compared with experimental observations. Future subjects to be considered such as how to connect the quantum system with the classical system in a more realistic manner, are also discussed.