The rapid integration of distributed solar photovoltaic (PV) generation is reshaping low-voltage distribution grids (LVDGs), creating voltage rise, reverse power flow, and congestion challenges for distribution system operators (DSOs). Flexibility in generation and demand, broadly understood as the capability to adjust generation or consumption in response to variability and uncertainty in net load, is increasingly central to cost-effective grid operation under high PV penetration. This review examines flexibility and controllability options in LVDGs, focusing on voltage regulation methods, supply- and demand-side flexibility resources, and market-based coordination mechanisms. The Norwegian Regulation on Quality of Supply (FoL) provides the regulatory context: it enforces 1 min average voltage compliance, stricter than the 10 min averaging window of EN 50160, making short-duration voltage excursions operationally significant and directly influencing the trade-off between curtailment, grid reinforcement, and local flexibility measures. Inverter-based active–reactive power control emerges as the most cost-effective overvoltage mitigation option, complemented by local battery energy storage systems (BESS) and demand response for congestion relief and energy shifting. Key gaps include limited LV observability, insufficient application of quasi-static time series (QSTS) assessment in planning, and underdeveloped DSO-aggregator coordination frameworks. Combined inverter control, feeder-end storage, and demand-side flexibility can defer costly reinforcements, particularly in rural 230 V IT feeders where voltage constraints dominate.