Molecular Dynamics (MD) is a computational microscope which enables the quantitative assessment of thermodynamic and dynamical behavior of chemical and biological systems. However, the spatiotemporal scales reachable via conventional MD render atomistic MD largely unable to appropriately probe biologically pertinent events computationally. Coarse-grained (CG) modeling expands these spatiotemporal scales through systematic elimination of atomistic degrees of freedom in favor of a CG molecular representation. Bottom-up CG modeling aims to develop an effective Hamiltonian which accurately recapitulates the statistical behavior of the CG degrees of freedom. In this work, bottom-up CG methods are developed and applied in a systematic manner to capture various aspects of lipid phase behavior. First, a general protocol for the development of CG lipid models which exhibit self-assembling behavior, the defining characteristic of amphiphiles, is developed. Second, we build upon this work to develop the first bottom-up CG models of simple lipid domains, i.e., ternary mixtures of bilayers in which cholesterol-induced phase separation is observed. We demonstrate a greater sampling efficiency for bottom-up CG models in comparison to top-down CG models. Third, we develop a machine-learning based virtual particle theory for CGing and demonstrate its utility in capturing solvent-mediated behavior, namely the membrane bending modulus, in implicit solvent models of lipid bilayers. Fourth, we develop an entropy-based approach for the variational optimization of ultra coarse-grained (UCG) ‘internal states’ as well as a relative entropy approach to UCG modeling. We apply these methods in tandem to develop a UCG model of a liquid-vapor interface as well as in capturing phase-coexistence in a ripple-phase bilayer. Lastly, we expand the bottom-up CG formalism to include bosonic and fermionic systems and establish the quantum analogue to the relative entropy principle of CGing and its semiclassical expansion.