Proteins are important biomolecules of life. Hence, understanding proteins' functions is important. Despite many biotechnological advancements, many proteins remain functionally unannotated. This dissertation aims to help advance the current understanding of proteins' functions by developing network-based computational approaches to study individual protein structures as well as physical interactions between proteins. Specifically, we use network representations of proteins at two different scales, as follows.First, we study biomolecular interactions within a protein using a protein structure network (PSN). In a PSN, nodes are amino acids of a protein, and edges capture amino acids' spatial proximities in the protein's 3-dimensional (3D) structure. We develop computational approaches for mining interesting PSN patterns, which we then use to quantify 3D protein structural similarities. Additionally, we use PSNs to study a specific protein folding-related phenomenon, i.e., to understand relationships between protein 3D structures and synonymous codon usage. Second, we study biomolecular interactions between proteins using a protein-protein interaction (PPI) network, where nodes are proteins and edges capture physical interactions between proteins. The current PPI network data of a given species is static. However, biological processes, including how cellular functioning changes with e.g., aging, disease progression, etc., are dynamic. Hence, dynamic PPI network data can potentially help improve our understanding of proteins' functions. We develop computational approaches for the inference and analysis of dynamic PPI networks and use them to study human aging.