An array of solid-state switches that link a source and load directly without a middle DC link make up matrix converters, bi-directional power electronic devices. Because of the intricacy of their control systems, matrix converters have historically had a limited industrial adoption. But in the last few years, the creation of simple and dependable commutation techniques has made matrix converter-based systems attractive substitutes for reactive power management. Comprehensive analysis of matrix converter control strategies for reactive power compensation is given in this work. We start with a summary of matrix converter technology. Subsequently, devices for the Flexible Alternating Current Transmission System (FACTS), systems for integrating renewable energy, and electric drives used for reactive power compensation during the past ten years are covered. An overview of direct and indirect matrix converter topologies is provided, together with an investigation of the several applications of these topologies for reactive power management. The performance of control strategies including model predictive control, space vector modulation, direct torque control, and others is then investigated and compared for reactive power compensation. At last, future study directions are noted. The research indicates that control methods and matrix converter technology have significantly advanced, indicating promise for more industrial reactive power compensation applications. Further expanding their reactive power compensation potential will be the ongoing development of cutting-edge matrix converter topologies and ever more complex control techniques.