Network Science has provided predictive models of many complex systems from molecular biology to social interactions. Most of this success is achieved by reducing multivariate dynamics to a graph of static interactions. Such network structure approach has provided many insights about the organization of complex systems. However, there is also a need to understand how to control them; for example, to revert a diseased cell to a healthy state in systems biology models of biochemical regulation. Based on recent work [1, 2] we show that the control of complex networks crucially depends on redundancy that exists at the level of variable dynamics. To understand the effect of such redundancy, we study automata networks− both systems biology models and large random ensembles of Boolean networks (BN). In these discrete dynamical systems, redundancy is conceptualized as canalization: when a subset of inputs is sufficient to determine the output of an automaton. We discuss two types of canalization: effective connectivity and input symmetry .