As the noise generation mechanism and acoustic control strategies for flapping wings remain largely unexplored, a hybrid method coupling the Farassat formulation 1A with the three-dimensional incompressible Navier-Stokes equations is developed to explore the aerodynamic and aeroacoustic performance of flapping wings as well as the effects of passive (trailing edge serrations, winglets, wingtip serrations) and active control (trailing edge flap motion). For a rectangular wing undergoing pitching and stroke motions in hovering flight at a Reynolds number (Re) of 310, results show that trailing edge serrations reduce the average sound power level within the Strouhal number (St) between 2 and 4 by 6.8 dB while the lift coefficient is almost the same. For a flapping wing with an elliptical cross-section at Re=8,800 in forward flight, winglets do not reduce the noise level but produce a positive lift coefficient of 0.19 and increase the propulsive efficiency by 6.8%. For a hovering flight wing with a rectangular profile at Re=7,040, winglets with a large cant angle decrease the power economy by 16% and the average sound power level over St =2 – 4 by 1.5 dB. Although wingtip serrations do not improve the aerodynamic performance, the average sound power level over St =2 to 4 is reduced by 2.0 dB. For a pitching NACA0012 foil with a flat plate trailing edge flap in forward flight at Re=100,000, the evolution of the dynamic stall vortex and the trailing edge vortex significantly affects its aerodynamic and aeroacoustic performance. Although trailing edge serrations do not significantly change the aerodynamic performance, a 4 dB reduction in the average sound pressure level over St = 1.25 to 4 is achieved. Trailing edge flap motion increases the average moment coefficient by about 12% and the lift to drag ratio by about 10% with no benefit for noise reduction.