Vortex-lattice solutions for unsteady aerodynamics on lifting surfaces are introduced. They provide a general description for aeroelastic applications with low-speed aircraft undergoing large wing deformations. The basic solution process is first outlined for 2-D problems, using a discrete vortex model for the fluid, and then extended to 3-D models using vortex rings. It is shown how this general solution can then be linearized around an arbitrary reference, and recast in state-space form. A compact form of the linear aerodynamic model is then introduce using methods of model-order reduction, and in particular, balanced realizations are seen to give a computationally-efficiency solution.