The plasmon resonance of a metal nanoparticle increases the optical field amplitude in and around the particle with respect to the incoming wave. In consequence, optical effects that are nonlinear in their field amplitude profit from this increased field. In general, a plasmonic structure can react nonlinearly by itself and it can also enhance the effect of the nonlinearity in its environment, which we consider as plasmonic nanoantenna. In this paper, we review third-order nonlinear effects such as third-harmonic generation, pump-probe spectroscopy, coherent anti-Stokes Raman scattering and four-wave mixing of and near plasmonic nanostructures. All these processes are described by very similar equations for the nonlinear polarization, but the underling physics differs.