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Low resolution coarse-grained (CG) models provide remarkable com- putational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to ma- chine learning methods. We then discuss recent approaches for si- multaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density- and temperature-dependence of these potentials. We also briefly dis- cuss exciting progress in modeling high resolution observables with low- resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understand- ing the limitations of prior CG models, but also for developing robust computational methods that resolve these limitations in practice.