Advanced Therapy Medicinal Products (ATMPs) are a novel class of biological therapeutics that utilise ground-breaking clinical interventions to prevent and treat life-threatening diseases. At the same time, viral vector-based and RNA-based platforms introduce a new generation of vaccine manufacturing processes. Their clinical success has led to an unprecedented rise in the demand that, for ATMPs, leads to a predicted market size of USD 9.6 billion by 2026. This paper discusses how mathematical models can serve as tools to assist decision-making in development, manufacturing and distribution of these new product classes. Recent contributions in the space of process, techno-economic and supply chain modelling are highlighted. Lastly, we present and discuss how Process Systems Engineering can be further advanced to support commercialisation of advanced therapeutics and vaccines.