The results of our recent experimental studies of magnetization-induced second- and third-order nonlinear optical effects in magnetic nanostructures are surveyed. Magnetization-induced variations of the intensity, the polarization state, and the relative phase of the second-harmonic wave are studied in magnetic nanogranular films, self-assembling films with garnet nanoparticles, thin magnetic metal films, and Langmuir-Blodgett films containing rare-earth ions. The nonlinear magneto-optical Kerr effect (NOMOKE) in second-harmonic generation (SHG) from thin magnetic and granular films is shown to exceed the linear magneto-optical Kerr effect by at least 1 order of magnitude. Magnetization-induced optical third-harmonic generation (THG) is observed in thin magnetic metal films and nanogranular films. The NOMOKE in THG from these magnetic nanostructures appears to be of the same order of magnitude as the second-order NOMOKE in SHG. The NOMOKE magnetic contrast in the THG intensity is up to ∼0.1 in Co_xAg(_1−x) nanogranular films. For the THG wave, the magnetization-induced rotation of polarization is up to 10° in thin Fe(110) films, and the relative phase shift is up to 70° in thin Co films. The studies of the magnetization-induced quadratic and cubic nonlinear-optical effects show the interconnection between the magnetic, structural, and magneto-optical properties of magnetic nanomaterials.