Abnormalities of biological processes in cells often lead to complex diseases. Thus, understanding biological processes is critical. With the proliferation of biotechnologies, large amounts of -omics data capturing different slices of cellular functioning are generated. Analyzing these large-scale -omics data via fast and scalable computational approaches has gained significant attention. A prominent direction for such computational analyses is to use biological networks, where nodes are biological entities and edges are interactions between these entities. This is because it is the complex interactions between the biological entities that carry out cellular functioning. However, first, not all -omics data are explicitly provided as networks. Instead, networks can be inferred from such -omics data, which is beneficial to at least implicitly capture the valuable interactions between biological entities. Second, even those -omics data that are explicitly provided as networks (e.g., protein-protein interactions) are not specific to a biological context of interest, such as disease, tissue, patient, or age. However, a context-specific network can be inferred by combining context-unspecific protein-protein interactions with other, context-specific non-network -omics data. The above two limitations emphasize the need for an important task in network biology -- that of network inference. Furthermore, given an (explicit or implicitly inferred) network, another important task in network biology is that of network analysis -- recognizing interesting network patterns that are relevant for a biological process of interest. This dissertation proposes novel computational approaches for both tasks -- network inference and network analysis -- in the context of studying two important biological processes -- human aging and malaria. First, regarding network biology research of human aging, we infer different types of (dynamic or static, weighted or unweighted) aging-specific networks. Then, we develop a supervised computational framework to systematically evaluate which network type performs the best in uncovering existing aging-related knowledge. Our hypothesis is that an aging-specific network that is both dynamic and weighted should be the most powerful and thus outperform all other (static or unweighted) network types. By relying on the best inferred aging-specific network(s), we can expand current knowledge about molecular mechanisms of the aging process, and hence better treat aging-related diseases. Second, regarding network biology research of malaria, we apply prominent network inference methods to infer gene co-expression networks. Then, we develop an unsupervised computational framework to systematically evaluate which network performs the best in uncovering existing functional annotations of genes in the malaria parasite, Plasmodium (P.) falciparum. By relying on the best inferred gene co-expression network(s), we can expand current functional knowledge about P. falciparum genes, and hence advance understanding of drug resistance in this species, which hinders the elimination of malaria.