Membranes composed of a lipid bilayer and embedded proteins are ubiquitous in nature. They form the barrier which demarcates every cell from its environment and separates the distinct organelles within eukaryotic cells, implicating membranes in a wide range of biological processes. The function of membranes and membrane proteins are determined by their structure, and the central focus of this thesis is the use of computational molecular dynamics simulations to study experimentally inaccessible details of membrane structure. Firstly, we have simulated ternary lipid bilayers containing steroids with a range of headgroup hydrophobicities, observing a correlation between the membrane lateral organization and the orientation of the steroid. Based on these results we suggest a general framework to distinguish previously identified steroid domain promoters and inhibitors. Secondly, we investigate the role of interleaflet coupling in membrane structure. This includes describing a compositional dependence to the interleaflet organization of phase separated membranes, as well as investigating structural perturbations due to interleaflet differences in composition. Thirdly, we demonstrate a strategy for obtaining experimental verification through low angle X-ray scattering and discuss its potential application to complex phase separated mixtures. The second focus of this thesis is considering how the structural features of membranes affect the behavior of membrane proteins. The membrane protein α-Synuclein is of wide interest due to its association with Parkinson's Disease, but its physiological function remains unknown. A third focus of this thesis is the structure of membrane-mimetics, such as detergent micelles and amphipathic polymers, which are commonly used for the stabilization of membrane proteins. Their potential distinct influence on protein behavior currently remains an unresolved hindrance to experimental characterization. The simulations presented herein demonstrate a distinct effect of membrane curvature on α-Synuclein behavior and suggest a potential role in regulating vesicle fusion. Collectively, these simulations of model systems offer insight into the fundamental features which determine the behavior of complex biological membranes.