To maximize conversion efficiency, photovoltaic (PV) systems generally operate in the maximum power point tracking (MPPT) mode. However, due to the increasing penetration level of PV systems, there is a need for more developed control functions in terms of frequency support services and voltage control to maintain the reliability and stability of the power grid. Therefore, flexible active power control is a mandatory task for grid-connected PV systems to meet part of the grid requirements. Hence, a significant number of flexible power point tracking (FPPT) algorithms have been introduced in the existing literature. The purpose of such algorithms is to realize a cost-effective method to provide grid support functionalities while minimizing the reliance on energy storage systems. This paper provides a comprehensive overview of grid support functionalities that can be obtained with the FPPT control of PV systems such as frequency support and volt-var control. Each of these grid support functionalities necessitates PV systems to operate under one of the three control strategies, which can be provided with FPPT algorithms. The three control strategies are classified as ① constant power generation control (CPGC), ② power reserve control (PRC), and ③ power ramp rate control (PRRC). A detailed discussion on available FPPT algorithms for each control strategy is also provided. This paper can serve as a comprehensive review of the state-of-the-art FPPT algorithms that can equip PV systems with various grid support functionalities.