Biologics represent the fastest growing sector of the pharmaceutical industry, yet their manufacture lags significantly behind that of small molecule drugs. This paper discusses the main product-related and process-related challenges during the development and production of therapeutic proteins, with particular focus on product heterogeneity and process monitoring and analytics. Emphasis is placed on novel contributions from the field of computational research that aim to enable the application of model-based process control strategies or are working towards the development of a digital twin of bioprocesses. Lastly, we review promising developments in the paradigm shift from batch to continuous processing.