Plasmonics provide us with an opportunity to achieve highly localized optical field in subwavelength scale and manipulate light artificially. Combining it with nonlinear optics gives birth to a new research field of nonlinear plasmonics. Among them, plasmonic second-harmonic generation (SHG) is of particular interest in both theory and application owing to its extraordinary characteristics. In this paper, we introduce origin of second harmonic generation from plasmonic structures based on the hydrodynamic model, and summarize the development and application of them, including enhancement of SHG from plasmonic resonances, enhanced SHG based on magnetic Lorentz force, manipulations of SHG radiation direction and frequency, and their applications in structure detection, sensing, and imaging. As a close remark, we provided an outlook for emerging platforms that are benefiting the plasmonic SHG.