Biomimetic systems with fine-tuned properties have many potential applications such as drug delivery systems or biosensors. In order to design such systems, one needs a detailed understanding of the underlying nanostructures and nanoprocesses. These structures are very thin and have a thickness of a few nanometers which makes them rather flexible and mobile. There is no experimental method by which one could directly image the dynamics of these structures. Therefore, it is rather appealing to use computer simulations in order to visualize these processes. A particularly powerful simulation method is provided by Dissipative Particle Dynamics which can be used to monitor supramolecular systems with a linear dimension of up to 50 nanometers over a time period of several microseconds. In this article, we discuss three examples for such systems: lipid membranes that contain several components and form different intramembrane domains; vesicles composed of diblock copolymers which could be used as drug delivery systems; and tension-induced fusion of bilayer membranes. The method of Dissipative-Particle-Dynamics can be used to optimize nanostructures and -processes in silico before one performs many costly experiments.