Bipartite networks are a useful way of representing interactions between two sets of entities. Understanding the underlying structures of such networks may give insights into the functionality and behaviour of the systems they represent. Two important structural patterns identified in bipartite networks are nestedness and modularity. Nestedness describes a hierarchical ordering of nodes such that more specialised nodes have interactions with a subset of the partners with which the more generalised nodes interact. Modularity captures the community structure of a network as distinct clusters of interactions, such that there are more connections within communities than between communities. While these network architectures are easy to describe in writing, their quantitative measurement for a given network is a difficult task. Several different methods have been proposed in each case and it is currently unclear which of them should be used in practice. This thesis considers the use, measurement and interpretation of nestedness and modularity in bipartite networks. First, it is shown how bipartite networks can be an effective tool for linking data and theory in community ecology, though use of a coevolutionary model of virus-bacteria interactions. Next, a series of studies is presented that push towards clarification of the best procedures to measure nestedness and modularity in bipartite networks. Robustness of nestedness measures is tested on a synthetic ensemble of networks, showing that apparent nestedness depends strongly on the choice of measure, null model and effect size statistics. Recommendations for performing nestedness are made with relation to individual and cross-network comparisons. Additionally, a new algorithm for identifying weighted modularity is proposed that can be shown to outperform existing methods. Crucially, it is shown that quantitative modular structures differ from traditional binary modular structures with implications for how modularity is reported and used. Improving the way in which nestedness and modularity are measured is a necessary step for integrating data and theory in bipartite networks.