Low resolution coarse-grained (CG) models are extensively employed for investigating mesoscale phenomena in soft materials. Nevertheless, it remains challenging to determine CG models that accurately describe both structure and thermodynamic properties since coarse-graining necessarily transfers entropy and information from the microstate distribution into the effective interactions between the remaining mesoscale degrees of freedom. We employ a simple analytic model in order to examine the intrinsic consequences of coarse-graining as a function of model resolution. Moreover, we demonstrate a variational method for parameterizing CG models from structural information via a generalized-Yvon-Born-Green (g-YBG) theory. This g-YBG theory is exact in principle and also determines accurate models for many complex systems in practice. In particular, we demonstrate an exceedingly coarse, but surprisingly accurate, g-YBG model for polyethylene oxide (PEO)-based ionomers. As time allows, we may present a framework for developing transferable CG models and demonstrate preliminary results for a transferable PEO-based ionomer model.