This report describes a combined theoretical and experimental program of research in the aerodynamics of supersonic lifting bodies. Analytical perturbation techniques are used to study the supersonic flow past slightly elliptical cones, cones whose cross-sections deviate slightly but arbitrarily from that of a right circular cone, cones of small longitudinal curvature, and right circular cones undergoing small harmonic pitching and/or plunging motions. These studies all involve perturbations of the well-known solution for supersonic flow past a right circular cone. Closed-form analytical results are achieved through the use of an approximation that accurately predicts results over the entire range of the hypersonic similarity parameter. These results give hypersonic limiting solutions that agree well with other independent analyses and, at the same time, agree exactly with linearized theory in the linear theory limit. Comparisons with experiment, where possible, also show good agreement.