In this paper we review several computational aerodynamics tools which we are using to examine and understand flapping flight. The computational methods incorporate different levels of geometric and physical modeling fidelity, ranging from simplified models which determine optimal wake vorticity distributions (eg. Hall et al. 1-3) to accurate descriptions of the flow physics. By exploiting multiple fidelity levels, computations can be efficiently performed at the required fidelity level making design and analysis a more efficient task. Several computational results are presented illustrating the versatility of the computational methods which are presented. The computational investigations explore top-down and bottom-up philosophies to enhance the understanding of flapping flight physics, force production and energetics. The results which are discussed range from simple two dimensional prescribed motions, to three-dimensional aerodynamics simulations of geometrically accurate bat flight.