At BIOMATH we develop and apply mathematical models and methodologies for the analysis and optimization of bio-processes. The focus is on mechanistic models which can be used to either build process knowledge (along with experimental monitoring) or optimize the process. The latter can be either with regard to operation or design. Depending on the objective, a different complexity model is to be used. We therefore use three modelling paradigms, i.e. computational fluid dynamics (CFD), population balance modelling (PBM) and bio-kinetics, as well as combinations. We make models of unit processes as well as process trains. In the frame of Industry 4.0 and digitalization, models with high predictive power become useful for them to be used in a real-time fashion as digital twins. Therefore, we also explore integrating mechanistic models with Machine learning tools to exploit the best of both worlds. Another application of digital twins is the development and implementation of classical (PID) and advanced process control.