We address the inverse problem of obtaining microscopic interaction potentials from macroscopic structure, here in the context of liquid-like systems. The proposed method uses a perturbation-theoretic formalism and requires noa prioriknowledge of the form of the potential. Very stable and rapidly converging potentials are obtained for widely different classes of fluids, and the results demonstrate the feasibility of inversion. The methodology can be extended to related problems in condensed matter physics and will aid in the analyses of structural data.