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Coarse-grain models provide an efficient means to simulate and investigate systems in which the desired behavior, property, or response is inherently at the mesoscale those that are both inaccessible to full atomistic representations and inapplicable to continuum theory. Granted, a developed coarse-grain model can only reflect the behavior included in their governing potentials and associated parameters, and consequently, the source of such parameters typically determines the accuracy and utility of the coarse-grain model. It is our contention that a complete theoretical foundation for any system requires synergistic multiscale transitions from atomic to mesoscale to macroscale descriptions. Hierarchical handshaking at each scale is crucial to predict structure property relationships, to provide fundamental mechanistic understanding, and to enable predictive modeling and material optimization to guide synthetic design efforts. Indeed, a finer-trains-coarser approach is not limited to bridge atomistic to mesoscopic scales (which is the focus of the current discussion), but can also refer to hierarchical parameterization transcending any scale, such as mesoscopic to continuum levels. Such a multiscale modeling paradigm establishes a fundamental link between atomistic behavior and the coarse-grain representation, providing a consistent theoretical approach to develop coarse-grain models for systems of various scales, constituent materials, and intended applications.