Aircraft noise is a key environmental concern for communities in the proximity of airports. Apart from being the source of severe nuisance and sleep disruption, aircraft noise has been linked to increasing risk for cardiovascular disease in segments of the affected population. While the engines remain the major source of noise in an aircraft, at low altitude and low speeds a very significant role is played by aerodynamic noise generated by airflow over the fuselage. During landing, when the engines operate at reduced power, a prominent source of aerodynamic noise is located at the landing gear bay, due to the occurrence of self-sustained oscillations in a resonant cavity. Suppressions of these oscillations would result in a significant reduction of overall aircraft noise during landing. In this talk, we summarize the research activity of the Gas Dynamics and Turbulence Lab at The Ohio State University that has been devoted to the design and experimental evaluation of model-based feedback controllers for suppressing subsonic cavity resonance. Proper orthogonal decomposition and Galerkin projection techniques were used to obtain a reduced-order model of the flow dynamics from experimental data. The model was made amenable to control design by means of an optimization-based control separation technique, which makes the control input appear explicitly in the equations. An adaptive feedback controller was then employed to suppress the cavity tones from pressure measurements. Experimental results, in qualitative agreement with the theoretical analysis, showed that the controller achieves a significant attenuation of the resonant tone with a redistribution of the energy into other frequencies. The benefits of parameter adaptation over controllers of fixed structure under varying or uncertain flow conditions were also demonstrated experimentally. Finally, an outlook into application of closed-loop strategies for jet noise mitigation is offered.