Biological cells are highly dynamic, and continually move material around their own volume and between their interior and exterior. Much of this transport encapsulates the material inside phospholipid vesicles that shuttle to and from, fusing with, and budding from, other membranes. A feature of vesicles that is crucial for this transport is their ability to fuse to target membranes and release their contents to the distal side. In industry, some personal care products contain vesicles to help transport reagents across the skin, and research on drug formulation shows that packaging active compounds inside vesicles delays their clearance from the blood stream. In this chapter, we survey the biological role and physicochemical properties of phospholipids, and describe progress in coarse-grained simulations of vesicles and vesicle fusion. Because coarse-grained simulations retain only those molecular details that are thought to influence the large-scale processes of interest, they act as a model embodying our current understanding. Comparing the predictions of these models with experiments reveals the importance of the retained microscopic details and also the deficiencies that can suggest missing details, thereby furthering our understanding of the complex dynamic world of vesicles.