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.