Near–field microscopy of second–harmonic generation combines high surface sensitivity of the nonlinear optical process and high spatial resolution of the near–field optics. It enables investigation of nonlinear optical phenomena at the nanoscale and provides an opportunity to develop a highly sensitive optical technique for materials characterization. In this paper we overview apertured and apertureless near–field approaches for local studies of second–harmonic generation. Near–field second–harmonic generation at metal surfaces and nanostructures and related electromagnetic field enhancement and confinement effects are considered. The latter demonstrates the feasibility of achieving nanoscale light sources using second–harmonic generation. Applications of second–harmonic near–field microscopy for characterization of magnetic and ferroelectric materials are also discussed. Nonlinear nano–optics can lead to the development of novel photonic devices on the sub–wavelength–scale as well as new tools for imaging and local optical studies of materials, chemical and biological species.