The number of proteins with known function is greatly dwarfed by the number of known proteins. Wet-lab experiments to determine protein function are costly in both time and resources. Thus, there is a need to computationally determine protein functions. As protein function is closely related to protein structure, in this thesis we describe two novel, network-based approaches for capturing, describing, and understanding protein structure. The first deals with the problem of protein structural classification. Recently, approaches that model protein 3D structures as networks have been positioned as a state-of-the-art solution for solving this problem. However, all existing network-based approaches approaches used a static network to capture the final, native structure of a protein for classification. Instead, our new approach uses a dynamic network to capture information about the emerging (sub)structure of a protein for classification. We find that our dynamic network-based approach greatly improves on the previous, static network-based approaches. This opens up future possibilities to explore protein folding-related research questions using dynamic, rather than static, PSNs. The second approach, also modeling protein 3D structures as networks, takes beginning steps to understand the relatively unknown role of synonymous codons in the protein folding process. Most amino acids are encoded for by more than one codon. The codons that encode a particular amino acid are called synonymous codons. Using synonymous codons, two different codon sequences can produce identical amino acid sequences. We are interested in studying whether which synonymous codon is used impacts the resulting protein 3D structure or fold. We study this by leveraging network-based centrality measures to determine trends describing the relative positions of synonymous codons in a protein. In the long run the work discussed in this thesis may contribute to understanding of how protein structure is folded.