Conventional wind farm operation, which prioritises power maximisation, is poorly aligned with the evolving requirements of modern power systems, characterised by increased asynchronous generation and reduced dispatchable capacity. This review uses Flexible Wind Farm Control as a term that encompasses control techniques that intentionally modulate wind farm output to better integrate wind energy with the grid. Focusing on European and UK contexts, the review examines how current policy frameworks, market structures, and system-needs are driving demand for new sources of flexibility. A comprehensive review of the literature is presented, covering key application areas of Flexible Wind Farm Control including frequency control, voltage support, fault ride-through, and integration within co-located and hybrid energy systems. Particular attention is given to rotor-side control strategies enabling power set-point tracking, synthetic inertia provision, and reserve-based operation. The review highlights differences in objectives, time scales, and system interactions for Wind Farm Control strategies that prioritise grid support over power maximisation. However, inconsistencies between policy and the recognised role of wind energy in providing flexibility remain clear. At the same time, much of the existing literature relies on simplified modelling approaches, highlighting the need for higher-fidelity models of turbine and farm dynamics, including turbulence, wake effects, and component fatigue, to better asses the performance of Flexible Wind Farm Control strategies. Overall, the literature suggests a persistent gap between policy and the technical capabilities of Flexible Wind Farm Control. Although some policy makers have acknowledged the potential of wind farms to support flexibility, significant work is required to fully identify and implement these capabilities in future power systems. Going forward, increased data availability, higher-fidelity simulation results, and field studies will be essential to establish wind farms as reliable providers of power system flexibility.