Biological membranes constitute a key component in all living cells and responsible for diverse, critical cellular processes, such as signaling, transport, and cell-cell communication. Understanding the biology of the cell and physiology of multicellular organisms, therefore, depends on our ability to describe the structure, dynamics, and function of biological membranes and their components (lipids and membrane proteins) at a detailed level. While modern experimental structural biological and biophysical techniques have substantially contributed to such an understanding, a large fraction of the molecular phenomena in biological systems are still inaccessible to experimental techniques. Computational methods, including molecular modeling and simulation, have been quite effective in complementing experiment by offering an approach that simultaneously provides the spatial and temporal resolutions needed for detailed description of cellular phenomena. In this talk, I will describe a number of recent computational studies in my lab investigating a variety of membrane-associated phenomena. In the first part, I will summarize our progress in employing non-equilibrium molecular dynamics simulation and advanced free energy methods to describe large-scale structural transitions in membrane transport proteins. Then I will present a number of cases in which we have focused on lipid-protein interactions and how these important effects modulate membrane protein structure, dynamics, and free energy landscapes associated with their function. Finally, I will present our most recent progress in cellular-scale modeling of biological membranes in their most realistic form, and advances in simulation of billion-atom super-molecular system. These studies have provided deep insight into the organization of biological membranes, and molecular interactions and processes within them that substantiate biological function.