Patterns of connectivity (structure) have been amply studied in network science and patterns of dynamics have been studied in dynamical systems theory. Still, much remains to be done to characterize redundancy and its importance for understanding and controlling the dynamics of complex systems---which, ultimately, defines their function. In this talk we will present our recent studies of redundancy in both the structure and dynamics of complex systems. The first concept we present is the invariant sub-graph that is revealed by the computation of all shortest paths (metric closure) of a weighted graph. We refer to this subgraph as the metric backbone of a complex network. The size of the backbone subgraph, in relation to the size of the original graph, defines the amount of redundancy in the network: edges not on this backbone are superfluous in the computation of shortest paths. We demonstrate the utility of the metric backbone with an analysis of social contact networks (via wearable sensors) used in epidemic spread models, as well as on other technological, brain, and gene regulation networks. The second concept stems from a dynamics perspective. We show that the control of complex networks crucially depends on redundancy that exists at the level of variable dynamics. To understand how control and information effectively propagate in such complex systems, we propose the effective graph which results after computation of effective connectivity in a discrete multivariate dynamical system. Finally, we discuss how we are demonstrating the utility of the approach with the analysis of a battery 50+ systems biology automata networks, including systems biology models of cancer.