Fluid flows exhibit complex dynamics over a range of spatial and temporal scales due to the intrinsic nonlinear interactions. Identification of important interactions in the flow field can reveal deeper insights into the physics and may enable interaction-based control of fluid flows. In an effort to understand and characterize the complex web of interactions present in the flow field, we consider the use of network and graph theoretic approaches for examining unsteady fluid flows. In this talk, we will discuss three representative problems to highlight the strength of this network-based approach to characterize, model, and control unsteady flows. We first consider the quantification of vortical interactions for clusters of discrete vortices and derive the sparsified dynamics model. The formulation is then extended to examine turbulent flows, revealing the structures of turbulence networks and their network characteristics. Furthermore, we identify kinetic energy transfer over a modal network in canonical unsteady flow through a networked oscillator representation. The modal interaction network is utilized to develop a feedback control design to stabilize the unsteady flow. From these examples, we demonstrate that the current network-based approaches are able to highlight important nonlinear interactions in the flow field that are not readily captured by traditional analyses and leverage that knowledge to perform feedback flow control.