Chinese hamster ovary (CHO) cells are the workhorse of the multibillion-dollar biopharmaceuticals industry. They have been extensively harnessed for recombinant protein synthesis, as they exhibit high titres and human-like post translational modifications (PTM), such as protein N-linked glycosylation. More specifically, N-linked glycosylation is a crucial PTM that includes the addition of an oligosaccharide in the backbone of the protein and strongly affects therapeutic efficacy and immunogenicity. In addition, the Quality by Design (QbD) paradigm that is broadly applied in academic research, necessitates a comprehensive understanding of the underlying biological relationships between the process parameters and the product quality attributes. To that end, computational tools have been vastly employed to elucidate cellular functions and predict the effect of process parameters on cell growth, product synthesis and quality. This thesis reports several advancements in the use of mathematical models for describing and optimizing bioprocesses. Firstly, a kinetic mathematical model describing CHO cell growth, metabolism, antibody synthesis and N-linked glycosylation was proposed, in order to capture the effect of galactose and uridine supplementation on cell growth and monoclonal antibody (mAb) glycosylation. Subsequently, the model was utilized to optimize galactosylation, a desired quality attribute of therapeutic mAbs. Following the QbD paradigm for ensuring product titre and quality, the kinetic model was subsequently used to identify an in silico Design Space (DS) that was also experimentally verified. An elaborate parameter estimation methodology was also developed in order to adapt the existing model to data from a newly introduced CHO cell line, without altering model structure. In an effort to reduce the burden of parameter estimation, the N-linked glycosylation submodel was replaced with an artificial neural network that was used as a standalone machine learning algorithm to predict the effect of feeding alterations and genetic engineering on the glycan distribution of several therapeutic proteins. In addition, a hybrid model configuration (HyGlycoM) incorporating the ANN-glycosylation model was also formulated to link extracellular process conditions to glycan distribution. The latter was found to outperform its fully kinetic equivalent when compared to experimental data. Finally, a comprehensive investigation of mAb galactosylation bottlenecks was carried out. Five fed-batch experiments with different concentrations of galactose and uridine supplemented throughout the culturing period, were carried out and were found to present similar mAb galactosylation. In order to identify the bottlenecks that limit galactosylation, further experimental analysis, including the investigation of glycans microheterogeneity of CHO host cell proteins (HCPs), was conducted. The experimental results were used to parameterize a novel and significant extension of the kinetic glycosylation model that simultaneously describes the N-linked glycosylation of both HCPs and the mAb product. Flux balance analysis was also used to analyse carbon and nitrogen metabolism using the experimental amino acid concentration profiles. In addition to the expression levels of the beta-1,4-galactosyltransferase enzyme, constraints imposed by the transport of the galactosylation sugar donor in the Golgi compartments and the consumption of resources towards HCPs glycosylation, were found to considerably influence mAb galactosylation.