The power system is experiencing an ever-increasing integration of photovoltaic power plants (PVPPs), which leads to the demand on the power system operators to force new requirements in order to sustain quality and reliability of the grid. Subsequently, a significant quantity of flexible power point tracking (FPPT) algorithms have been proposed in the literature to enhance functionalities of PVPPs. The intention of FPPT algorithms is to regulate the PV power to a specific value imposed by the grid codes and operational conditions. This will inevitably interfere the maximum power point tracking (MPPT) operation of PV systems. Nevertheless, the FPPT control makes PVPPs much more grid-friendly. The main contribution of this article is to comprehensively compare available FPPT algorithms in the literature from different aspects and provide a benchmark for researchers and engineers to select suitable FPPT algorithms for specific applications. A classification and short description of them are provided in this article. The dynamic performances of the investigated algorithms are compared with experimental tests on a scaled-down prototype. Directions for future studies in this area are also presented.