<p>Reduced-gravity flight is a critical enabler for microgravity research, technology demonstration, and human spaceflight preparation. Among available platforms, aircraft performing parabolic maneuvers provide a practical and repeatable means of generating short-duration reduced-gravity environments. Achieving precise and sustained <i>g</i>-level profiles during these maneuvers, however, poses significant challenges due to nonlinear aircraft dynamics and environmental disturbances. This paper presents a comprehensive survey of control methodologies for reduced-gravity flight, covering manned aircraft, fixed-wing UAVs, and multirotor systems. The review traces the evolution from early nonlinear and gain-scheduled approaches to advanced acceleration-feedback architectures designed for improved robustness and disturbance rejection. Each method is examined in terms of control structure, implementation complexity, and performance metrics, including residual acceleration and maneuver duration. Validation strategies, ranging from high-fidelity simulation and hardware-in-the-loop testing to real-flight demonstrations, are compared to assess technological maturity. Key gaps are identified, including the absence of full-scale autonomous parabolic flights, and future research priorities are outlined in adaptive and fault-tolerant control, trajectory optimization, and airframe design innovations to enable reliable, autonomous reduced-gravity operations. Beyond surveying methods, this review codifies application requirements, distills recurring control challenges into design patterns, and offers concise practitioner guidance that links controller choices to reported residual-<i>g</i> performance across platforms.</p>