Second harmonic (SH) generation (SHG) in plasmonic nanostructures originates from the surface of centrosymmetric metals where inversion symmetry is broken. The interest in that topic stems from the strong near-field enhancement on the surface of plasmonic nanostructures when the corresponding surface plasmon resonance is excited under far-field illumination, which can greatly increase the SH polarization in a deep subwavelength area, the so-called plasmonic hot spot (an area where the field is enhanced by several orders of magnitude). Furthermore, the SH emission is highly sensitive to the geometrical changes in the plasmonic system. Thus, the emission pattern of SHG can be drastically modified by the size and shape of plasmonic nanoantennas. In this thesis, different plasmonic effects are investigated and demonstrated in conjunction with the design of nonlinear metasurfaces to enhance and manipulate SHG. In the first work reported therein, we study the mechanisms of SH enhancement in double-resonant aluminum nanoantennas supporting plasmonic dipolar modes at both fundamental and SH wavelengths. For this purpose, the plasmonic dipolar resonance at the fundamental wavelength was first optimized by an appropriate length of the long bar of DRAs, while the short bar length was changed in a way such that the supported plasmonic dipolar mode can be tuned around the SH wavelength. The maximum SH intensity is clearly observed in the case when the short bar supports a plasmonic dipolar mode at the SH wavelength. The SH near-field distribution clearly confirms that the maximum enhancement of SHG is reached when the near-field coupling between the SH quadrupolar mode and SH dipolar mode is the strongest. In the second work, we combine both experiments and SIE simulations to investigate ultra-thin metasurfaces composed of 3D gold nanopillars, which enable the control of the dependency of induced nonlinear polarization upon the incident wavevector of excitation light. By changing the tilted angle of 3D gold nanopillars, the asymmetric nonlinearity of the metasurface is investigated in details using a homebuilt flexible nonlinear Fourier microscope. Interestingly, a variation of the SH intensity close to 80 is measured for opposite illumination angles, revealing a very high asymmetry in the SH response of the nanopillar metasurfaces. This work paves the way for the optimal design of directional nonlinear plasmonic meta-mirrors. Finally, we propose a reflective phase-gradient metasurface that can convert a free-space propagating wave into an unidirectional hybrid surface plasmon wave supported on its silver backplate with nearly 80% absorption efficiency at a 800 nm excitation wavelength, leading to a SH enhancement as high as 235 folds in the measurements. The phase-gradient metasurface is designed and optimized to support an anomalous reflection channel at 800 nm following the generalized Snell's law. The unidirectional and confined propagation for the hybrid plasmon mode can boost the light-matter interactions along the in-plane direction. Interestingly, the single-channel SH emission governed by the SH phase-matching condition reveals the relationship of SH emission channel and excited hybrid plasmon mode in the designed metasurface. This work provides a new scheme to enhance the SH efficiency by in-plane SH phase matching in the subwavelength-thick nonlinear metasurfaces.