The first systematic account is presented of the current status of the problem of inverse electronic relaxation under the conditions of multiphoton excitation with infrared laser radiation, which converts a strong vibrational excitation of a molecule into an electronic excitation and gives rise to ultraviolet or visible radiation. This review deals with the fundamental principles of the appearance of inverse electronic relaxation in isolated molecules. An analysis is made of the characteristics of visible radiation generated by this relaxation process. Current ideas are used in a detailed investigation of those characteristics of infrared multiphoton excitation which determine inverse electronic relaxation. An account is given of the recently developed experimental methods for attribution of the observed radiation to a specific particle (molecular fragment). These methods include time-of-flight spectroscopy and separation of successive stages of the emission process in accordance with the laser radiation energy density. A critical analysis is made of the numerous experimental observations of collisionless visible radiation resulting from multiphoton excitation by infrared laser radiation. Some of the most thoroughly investigated molecules are used to consider the cases of inverse electronic relaxation resulting from multiphoton excitation of specific molecules and radicals, particularly SO$_2$ and OsO$_4$. Apart from inverse electronic relaxation, attention is given to another nonadiabatic process occurring in the case of infrared multiphoton excitation, which is the detachment of electrons from molecular ions induced by CO$_2$ laser radiation. The review covers the work published up to September 1986.