As the most common nonlinear optical process, second harmonic generation (SHG) has important application value in the field of nanophotonics. With the rapid development of metal nanomaterial processing and chemical preparation technology, various structures based on metal nanoparticles have been used to achieve the enhancement and modulation of SHG. In the field of nonlinear optics, plasmonic metal nanostructures have become potential candidates for nonlinear optoelectronic devices because of their highly adjustable physical characteristics. In this article, first, the basic optical principles of SHG and the source of surface symmetry breaking in metal nanoparticles are briefly introduced. Next, the related reports on SHG in metal nanostructures are reviewed from three aspects: the enhancement of SHG efficiency by double resonance structures, the SHG effect based on magnetic resonance and the harmonic energy transfer. Then, the applications of SHG in the sensing, imaging and in situ monitoring of metal nanostructures are summarized. Future opportunities for SHG in composite systems composed of metal nanostructures and two-dimensional materials are also proposed.