Social insect colonies (ants, bees, wasps, and termites) show sophisticated collective problem-solving in the face of variable constraints. Individuals exchange information and materials such as food. The resulting network structure and dynamics can inform us about the mechanisms by which the insects achieve particular collective behaviors and these can be transposed to man-made and social networks. We discuss how network analysis can answer important questions about social insects, such as how effective task allocation or information flow is realized. We put forward the idea that network analysis methods are under-utilized in social insect research, and that they can provide novel ways to view the complexity of collective behavior, particularly if network dynamics are taken into account. To illustrate this, we present an example of network tasks performed by ant workers, linked by instances of workers switching from one task to another. We show how temporal network analysis can propose and test new hypotheses on mechanisms of task allocation, and how adding temporal elements to static networks can drastically change results.We discuss the benefits of using social insects as models for complex systems in general. There are multiple opportunities emergent technologies and analysis methods in facilitating research on social insect network. The potential for interdisciplinary work could significantly advance diverse fields such as behavioral ecology, computer sciences, and engineering.