The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from extremely weak nature and require high input intensity values in order to be excited... Interestingly, the large third order nonlinearity of graphene, along with the strong field confinement stemming from its plasmonic behavior, can be utilized to enhance several relative weak nonlinear effects at infrared (IR) and terahertz (THz) frequencies. Towards this goal, various nonlinear graphene metasurfaces are presented in this work to effectively increase the efficiency of different optical nonlinear effects and, as a result, decrease the required input intensity needed to be excited. In particular, we will show that the efficiency of four-wave mixing (FWM) can be improved by several orders of magnitude by using a nonlinear metasurface composed of patterned graphene ribbons, a dielectric interlayer, and a metallic reflector acting as substrate. We also demonstrate that the self-phase modulation (SPM) nonlinear process can be enhanced by using an alternative graphene nonlinear metasurface, operating as coherent perfect absorber, leading to a pronounced shift in the resonant frequency of the coherent perfect absorption (CPA) effect of this structure as the input intensity of the impinging incident waves is increased. This property will provide a robust mechanism to dynamically tune and switch the CPA process. Furthermore, it will be presented that strong negative reflection and refraction can be achieved by a single graphene monolayer film due to the enhancement of another nonlinear process, known as phase conjugation. This nonlinear process is envisioned to be used in the construction of a perfect imaging device with subwavelength resolution. (read more)