Chinese hamster ovary (CHO) cells are used for the production of the majority of biopharmaceutical drugs, and thus have remained the standard industry host for the past three decades. The amino acid composition of the medium plays a key role in commercial scale biologics manufacturing, as amino acids constitute the building blocks of both endogenous and heterologous proteins, are involved in metabolic and non-metabolic pathways, and can act as main sources of nitrogen and carbon under certain conditions. As biomanufactured proteins become increasingly complex, the adoption of model-based approaches become ever more popular in complementing the challenging task of medium development. The extensively studied amino acid metabolism is exceptionally suitable for such model-driven analyses, and although still limited in practice, the development of these strategies is gaining attention, particularly in this domain. This paper provides a review of recent efforts. We first provide an overview of the widely adopted practice, and move on to describe the model-driven approaches employed for the improvement and optimization of the external amino acid supply in light of cellular amino acid demand. We conclude by proposing the likely prevalent direction the field is heading towards, providing a critical evaluation of the current state and the future challenges and considerations.