Metallic nanoparticles support collective oscillations of conduction-band electrons, in response to light incidences. Such phenomenon is called localized surface plasmons, which confine large electromagnetic fields in sub-wavelength dimensions, enabling the light manipulation at the nanoscale. Plasmonic nanoparticles have established many promising applications, such as infrared photodetections, photothermal generation steam, chemical photocatalysis, cancer therapy and surface-enhanced spectroscopy. More interesting, plasmonic nanostructures could generate strong nonlinear-optical effects by relatively low excitation powers, and have been widely used in different processes like second-harmonic generations (SHG), difference-frequency generation (DFG), third-harmonic generation (THG), optical four-wave mixing (FWM) and surface-enhanced Raman scattering (SERS). This thesis will focused on two types of second-order and two types of third-order nonlinear-optical processes, enhanced by artificial plasmonic nanostructures. Firstly, the second-harmonic generation on a single nanocup is studied, and the signal is demonstrated to have increasing intensity as the 3D symmetry of the nanocup is reduced. Then, optical four-wave mixing is generated on a plasmonic nanocluster which supports a coherent oscillation of two Fano resonances. The electric fields from both Fano resonances add coherently resulting in strong fields and correspondingly large signals. This nanocluster has a large color-conversion efficiency, and could be used for building blocks of optical processors that convert two input colors into a third color. Later, one specific application of four-wave mixing, the coherent anti-Stokes Raman scattering (CARS) is studied. By exploiting the unique light harvesting properties of a Fano resonance of a specially designed nano-quadrumer, the surface-enhanced CARS (SECARS) technique amplifies the Raman signals of molecules on the quadrumer by about 100 billion times. This enables the accurate identification of a single molecule with less than 20 atoms. Finally, a plasmon-enhanced optical parametric amplifier (OPA) is designed: A BaTiO3 nanosphere is used as the nonlinear OPA medium; A nanoshell wrapping this nanosphere is used as a triply resonant cavity for all the pump, signal and idler beams; The generated idler beam has a wide tuning range in the near-infrared by changing the delay between the narrowband pump beam and broadband signal beam. This surface-plasmon-enhanced OPA could be an efficient light source working in the infrared regime, with large wavelength tunabilities and nanoscale dimensions easily integrated into the next-generation optoelectronic devices.