Grid-connected PV inverters require sophisticated control procedures for smooth integration with the modern electrical grid. The ability of FCS-MPC to manage the discrete character of power electronic devices is highly acknowledged, since it enables direct manipulation of switching states without requiring modulation techniques. This review discusses the latest approaches in FCS-MPC methods for PV-based grid-connected inverter systems. It also classifies these methods according to control objectives, such as active and reactive power control, harmonic suppression, and voltage regulation. The application of FCS-MPC particularly emphasizing its benefits, including quick response times, resistance to changes in parameters, and the capacity to manage restrictions and nonlinearities in the system without the requirement for modulators, has been investigated in this review. Recent developments in robust and adaptive MPC strategies, which enhance system performance despite distorted grid settings and parametric uncertainties, are emphasized. This analysis classifies FCS-MPC techniques based on their control goals, optimal parameters and cost function, this paper also identifies drawbacks in these existing control methods and provide recommendation for future research in FCS-MPC for grid-connected PV-inverter systems.