We survey the main results of recent studied of the nonlinear optical effects in metasurfaces that reveal pronounced plasmonic effects. Optical second harmonic generation and two-photon absorption, plasmon-induced spatial localization of the optical field. nonlinear magnetooptical effects in magneto-plasmonic scystals are discussed. We demonstrate a number of examples demonstrating advantages of the nonlinear-optical diagnostics tools for the visualization of tiny properties of nanostructures.