Theoretical and numerical models and methods to study and understand complex soft matter and biomimetic and biological systems -- on the basis of physical principles -- are developed in the group of Gerhard Gompper. Here, the addressed issues range from the structure and dynamics of synthetic and biological macromolecules, the interactions of proteins and nanoparticles with membranes, and the shapes and deformations of (blood) cells under flow, to the non-equilibrium dynamics of the cytoskeleton, the motion and flow generation of microswimmers (like bacteria, sperm, cilia, and artificial self-propelled particles), and growing tissues. A significant part of the investigations is performed by large-scale numerical simulations on super-computers. In particular, mesoscale hydrodynamics simulation techniques are utilized to capture the dynamics of systems in aqueous environments.