When light field interacts with metamaterials, both the electric field and the magnetic field must be considered. The dispersive permeability of metamaterials induces many new characteristics under the nonlinear interaction between light field and metamaterials. The research progresses on the second-order nonlinear optical phenomena are briefly described, and some research results on the propagation characteristics of electromagnetic waves in the metamaterials with third-order nonlinear optical responses are specially presented, such as the establishment of the propagation model, the results for modulation instabilities, solitons, self-focusing.