Industrialization of mammalian cell culture has been achieved by integrating knowledge from several applying core concepts of chemical engineering, cellular and molecular biology, and biochemistry. Modeling has been applied to biological and physical processes to gain additional insights into such processes. This article covers modeling of the bioreactor and metabolic processes as it applies to bioprocess. Hydrodynamics of a bioreactor is briefly described while additional focus is given to gas-liquid mass transfer. Biological modeling is presented in the order of increasing complexity. First steady state models are presented followed by dynamic models, cybernetic models, and finally bioreactor integrated models. The closing discussion summarizes challenges of implementation of model-based approaches in the biopharmaceutical industry. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 398-408, 2017