The properties of optical resonators with quality-factor Q⩾108, effective volume of e.m. field localization Veff≈10−9 cm3 and threshold power of optical bistability Wbist≈10−5 W are described. The prospects to reduce Veff and Wbist are discussed. With possible reduction of controlling energy of optical switching down to a single quantum and employment of the monophotonic states of light, the whispering-gallery microresonators can open the way to realize Feynman's quantum-mechanical computer.