The development of physics-based noise prediction tools for analysis of aerodynamic noise sources is of paramount importance since noise regulations have become more stringent. Direct simulation of aerodynamic noise remains prohibitively expensive for engineering problems because of the resolution requirements. Therefore, hybrid approaches that consist of predicting nearfield flow quantities by a suitable CFD simulation and farfield sound radiation by aeroacoustic integral methods are more attractive. In this work, we apply the fast multipole method (FMM) to accelerate the solution of boundary integral equation methods such as the boundary element method (BEM) and the Ffowcs Williams & Hawkings (FWH) acoustic analogy formulation. The FMM-BEM is implemented for the solution of acoustic scattering problems and the effects of non-uniform potential flows on acoustic scattering are investigated. The FMM-FWH is implemented for the solution of two and three-dimensional problems of sound propagation. The effects of flow convection and non-linear quadrupole sources are assessed through the study of sound generated by unsteady laminar flows. Finally, a hybrid methodology is applied for the investigation of airfoil noise. This study is important for the design of aerodynamic shapes such as wings and high-lift devices, as well as wind turbine blades, fans and propellers. The present investigation of airfoil self-noise generation and propagation concerns the broadband noise that arises from the interaction of turbulent boundary layers with the airfoil trailing edge and tonal noise that arises from vortex shedding generated by laminar boundary layers. Nearfield acoustic sources are computed using compressible large eddy simulation (LES) and acoustic predictions are performed by the FMM-FWH. Numerical simulations are conducted for a NACA0012 airfoil with tripped boundary layers and blunt rounded trailing edge at different Mach numbers and angles of incidence. The effects of non-linear quadrupole sources and convection are assessed. In order to validate the numerical solutions, flow simulation and acoustic prediction results are compared to experimental data available in the literature and excellent agreement is observed.