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The still increasing penetration of power electronics into the modern power systems challenges the entire system stability, which requires more advanced control strategies to address the issues. One of the challenges is the variability of renewable energies, including photovoltaic (PV) systems, which are generally operating with uncertainty and intermittency (non-dispatchable). In this regard, flexible power control solutions are of interest for PV systems, as an essential function of smart PV inverters, to minimize the adverse impact in grid-integration and operation. On the other hand, PV systems can be adapted to provide ancillary services, e.g., voltage and frequency support through the power control. This paper thus presents an overview of the recent advances in flexible active power control (FAPC) that enables the grid-friendly integration of smart PV systems. The demands for the FAPC are introduced from the grid's perspective. Then, various FAPC schemes are reviewed, among which the control strategy by modifying the maximum power point tracking (MPPT) is the most feasible and efficient without any hardware modifications. This is known as the flexible power point tracking (FPPT), which is further illustrated by case studies. Additionally, a power reserve control (PRC) facilitating comprehensive voltage and frequency support to the grid is discussed in detail. Future research perspectives are also presented.