Inferring internal scattering parameters for general, heterogeneous materials, remains a challenging inverse problem. Its difficulty arises from the complex way in which scattering materials interact with light, as well as the very high dimensionality of the material space implied by heterogeneity. The recent emergence of diverse computational imaging techniques, together with the widespread availability of computing power, present a renewed opportunity for tackling this problem. We take first steps in this direction, by deriving theoretical results, developing an algorithmic framework, and performing quantitative evaluations for the problem of heterogeneous inverse scattering from simulated measurements of different computational imaging configurations.