Substantial work has been done to elucidate the errors that occur upon coarse-graining and their impact on simulated CG properties. In brief, coarse-graining results in reducible and irreducible types of errors associated with reproducing the atomistic potential energy surface (PES). The irreducible errors arise from the fact that CG models are incapable, by definition, of capturing the energy and force variance associated with the excised degrees of freedom. Put differently, a CG configuration maps to many inequivalent atomistic configurations with distinct energies and forces. Schemes have been proposed for estimating the missing variance and introducing it stochastically into the CG dynamics. Nevertheless, short of simulating the atomistic system directly, some amount of irreducible error is intrinsic in the forces and energies of a CG model. Thus, what so-called "bottom-up" CG models generally try and reproduce are the expected (i.e., Boltzmann averaged) forces and energies of each configuration. Since these are state dependent, the transferability of CG potentials to other state points is not guarranteed unless these quantities adventitiously exhibit no temperature/pressure dependence over the simulated ranges, or unless an additional state-dependence is added to the CG model. In contrast, "top-down" CG models dispense with trying to formally reproduce the Boltzmann averaged potential energy surface (PES) and instead just pheneomenologically attempt to reproduce a subset of simulated properties. Since top-down models are only qualitatively related to specific atomistic systems they are not further discussed here.