Several panel methods are developed to model subsonic aerodynamics. The vorticity panel method for two-dimensional problems is capable of handling general unsteady, potential, lifting flows. The lifting surface is modelled with a vortex sheet and the wakes by discrete vortices. As an imitation of the conditions at the trailing edge, stagnation conditions on both surfaces are used. The over-determined system is solved by an optimization scheme. The present predictions are in good agreement with experimental data and other computations. Moreover the present approach provides an attractive alternative to those developed earlier. Two panel methods for three-dimensional nonlifting problems are developed. One uses source distributions over curved elements and the other vorticity distributions over flat elements. For the source formulation, the effect of weakly nonlinear geometry on the numerical results is shown to accelerate the convergence of numerical values in general. In addition, the extensive comparisons between two formulations reveal that the voticity panel method is even more stable and accurate than the curved source panel method. Another vorticity panel method is developed to study the lifting l flows past three-dimensional bodies with sharp edges. The body is modelled by single vortex sheet for thin bodies and two vortex sheets for thick bodies while the wakes are modelled with a number of strings of discrete vortices. The flows are assumed to separate along the the sharp edges. The combination of continuous vorticity on the lifting surface and discrete vortices in the wakes yields excellent versatility and the capability of handling the tightly rolled wakes and predicting continuous pressure distributions on the lifting surface. The method is applied to thin and thick low-aspect-ratio delta wings and rectangular wings. The computed aerodynamic forces and wake shapes are in quantitative agreement with experimental data and other computational results. / Ph. D.