All species interact with other species to form complex networks of connections. Such networks are a powerful way to represent ecological communities because they describe (i) the roles of individual species and (ii) the structure of the community as a whole in a single framework amenable to mathematical and computational analysis. In this thesis I consider a number of outstanding problems in network ecology. In Chapter 1, I examine the consequences for network structure of removing non-mutualistic interactions from plant-frugivore visitation networks. I find that plant-frugivore visitation networks act as a good proxy for mutualistic seed dispersal networks in terms of whole-network topology, but not when considering species- level structures. Chapter 2 deals with whether generalisation drives abundance or vice versa in plant-hummingbird pollination networks. I find evidence that abundance drives generalisation and use a simple model to show that neutral processes can explain broad patterns of species- level generalisation. In Chapter 3, I quantify the importance and vulnerability of mutualistic interactions to understand the risk that interaction extinction poses to communities. I conclude that (i) the interactions most important for community stability are those which are most vulnerable to extinction, and (ii) important and vulnerable interactions tend to be important and vulnerable wherever they occur. In Chapter 4, I consider motifs as an alternative to indices for characterising the structure of bipartite networks. I find that motifs capture significantly more information about network topology than indices and advocate adding bipartite motifs to the suite of analytical tools used by network ecologists. Chapter 5 describes a software package in R, MATLAB and Python for conducting motif analyses of bipartite networks. It uses novel mathematical formulations to dramatically reduce the computational time required for motif calculations compared to competing software.