In the developing field of nonlinear plasmonics, it is important to understand the nonlinear responses of the metallic nanostructures. In the present thesis, rigorous electrodynamical simulations based on the fully vectorial three-dimensional nonlinear hydrodynamic Drude model describing metal coupled to Maxwell's equations are performed to investigate linear and nonlinear responses of the plasmonic materials and their coupling with quantum emitters.The first part of this thesis is devoted to analyzing properties of the localized surface plasmon resonances of metallic nanostructures and their nonlinear optical responses. The behavior of the second harmonic is investigated as a function of various physical parameters at different plasmonic interfaces, revealing highly complex dynamics. By collaborating with several research teams, simulations are proven to be in close agreement with experiments, both quantitative and qualitative. The second part of the thesis explores the strong coupling regime and its influence on the second harmonic generation. Considering plasmonic systems of molecules and periodic nanohole arrays on equal footing in the nonlinear regime is done for the first time. The results obtained are supported by a simple analytical model.