Molecular dynamics simulations provide critical insights into molecular mechanisms underlying cellular processes. Most such processes, however, remain out of reach, due to large system sizes and long time scales involved. This thesis describes molecular dynamics simulations of large macromolecular complexes on relevant time scales, using a simplified, or "coarse-grained" description. The method developed for this purpose, called shape-based coarse-graining, is applied to a number of systems. Simulations of several viruses, including the first all-atom simulation of a complete virus, reveal how interlocking between viral coat proteins determines virus's stability. In simulations of the rotating bacterial flagellum, we find that solvent-protein interactions are likely to contribute to the formation of the flagellum's polymorphic helical shapes. A computational study at four levels of resolution is performed to investigate concerted action of multiple BAR domain proteins, which sculpt curved membranes in cells. Various arrangements of BAR domains on the membrane surface are found to lead to distinct membrane curvatures and bending dynamics. Also, a study on a much larger scale is performed, where a theoretical-computational framework is developed to investigate suitability of the 4Pi microscopy, an approach that improves resolution of a light microscope in comparison with conventional microscopy, for measurements of molecular mobility. The developed framework is validated by measurements on model systems and allows us to investigate a limit for light focusing in the microscopy setups similar to the 4Pi type. Overall, the computational methods developed provide tools for simulations of system sizes and time scales that have not been accessible before, and, combined with experiments and all-atom simulations, can describe dynamics of many biological systems with a high level of detail.