Numerous innovations in photonics were realized on the base of nonlinear optical properties and notably in information technologies. To take advantage of nonlinear optical properties of glass, multidisciplinary research efforts were necessary combining optics, glass chemistry, material science as well as development of optical or electrical polarizations processes. This chapter addresses both fundamental aspects of the nonlinear optical responses, but also the exploitation of nonlinear optical phenomena in glassy material. It starts by a general introduction on nonlinear optical phenomena and concepts. Then, the specific cases of second and third optical responses in glasses are treated separately and described in details as a function of the corresponding optical phenomena, the different glass families and the applications.