Coarse-grained (CG) models provide a promising computational tool for investigating slow complex processes that cannot be adequately studied using more detailed models. However, unless the CG model is consistent with an accurate high-resolution model, the results of CG modeling may be misleading. The present talk describes a statistical mechanical framework that provides a rigorous “multiscale bridge” connecting models with different resolution. In particular, this framework provides a formal definition of consistency and a systematic computational methodology for constructing a coarse-grained (CG) model that is consistent with a particular atomistic model. The cornerstone of this approach is a variational principle for calculating a many-body potential of mean force, which is the appropriate potential for such a consistent CG model. The multiscale coarse-graining method employs this variational principle by numerically calculating the projection of the atomistic force field onto the subspace of CG force fields spanned by a given set of basis vectors. Because typical CG force field basis vectors correspond to correlated molecular interactions, these basis vectors are not orthogonal and, consequently, many-body correlation functions must be explicitly treated. The present talk describes this development, presents numerical applications for molecular systems, and demonstrates how this framework may be employed to develop transferable CG interaction potentials.