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Computational modeling of lipids at the atomistic level provides insights into the chemical physics of biological membranes and opens the possibility to model membrane-protein interactions. This dissertation presents contributions to the CHARMM/Drude family of lipid force fields and applications of the CHARMM36 lipid force field to model membranes.Long-range Lennard-Jones interactions are critical for membrane simulations but were excluded from the CHARMM lipid force field for historical reasons. Re-parameterization of the CHARMM36 (C36) lipid force field for phosphatidylcholine, phosphatidylethanolamine, phosphatidylglycerol, and ether lipids is performed to incorporate these interactions through the Lennard-Jones particle-mesh Ewald (LJ-PME) method. The resulting force field is denoted C36/LJ-PME. C36/LJ-PME is in excellent agreement with experimental structure data for lipid bilayers and reproduces the experimental compression isotherm of monolayers. A semi-automated protocol is developed and used during this parameterization and significantly accelerates the whole process. The same protocol is used for the optimization of the Drude polarizable lipid force field. The optimization of this force field focuses on the structural and mechanical properties of bilayers and ab initio results of model compounds representing the lipid headgroup. Long-range dispersion interactions are incorporated into the force field as well. The resulting force field is validated against more structural and dynamic properties of bilayers and the compression isotherm of monolayers and demonstrates significant improvements over the past versions of the force field. In addition to these fully atomistic models, this dissertation also discusses the update to the CHARMM36 united atom chain model. Both the original model (C36UA) and the revised model (C36UAr) adopt the all-atom C36 lipid force field parameters for the headgroup and a united atom representation for the chain. The update focuses on the Lennard-Jones parameters of the hydrocarbon chain and related dihedrals. Bulk liquid properties (density, heat of vaporization, isothermal compressibility, and diffusion constant) of linear alkanes and alkenes and ab initio torsional scans are used as initial fitting targets. Bilayer surface area is used to fine-tune the dihedral parameters. Bilayer simulations of various headgroups and tails using C36UAr demonstrate significant improvements over C36UA from a structural perspective. The last part of this dissertation presents the applications of the C36 lipid force field. The inner membrane of Pseudomonas aeruginosa (P. aeruginosa) is modeled in two modes (planktonic and biofilm) to study the influence of lipid composition on bilayer structural and mechanical properties. The hydrophobic thicknesses of the model membrane agree with the P. aeruginosa transmembrane proteins in the Orientations of Proteins in Membranes (OPM) database. Symmetric and asymmetric models for the Arabidopsis thaliana plasma membrane are modeled. Molecular dynamics (MD) simulations indicate that the outer leaflet is more rigid and tightly packed to the inner leaflet. The interplay between glycolipids and sterols is found to be critical in lipid clustering and a possible mechanism for lipid phase separation has been proposed.