Abstract: Many real world systems utilize networks of mechanical, electrical, or informational signals to perform complex functions. Recent advances across multiple disciplines have begun to elucidate the role that these networks play in constraining and enabling system dynamics. A critical remaining challenge is to harness the predictive role of complex networks to support the control, rescue, and imitation of system function. Such predictions can be extracted from network structure, network dynamics, or the properties of the signals that propagate through the network. I will illustrate these efforts and the associated mathematical tools they employ using examples drawn from physical, biological and social systems. For example, the network structure of soft materials constrains sound propagation, informing the development of non-destructive testing and design techniques. The network dynamics of human brain activity predicts adaptive behaviors like learning, potentially enabling the monitoring of disease progression and rehabilitation. The information passed between individuals on a social network drives collective behavioral variability by altering decision dynamics, impacting information dissemination policies. I will discuss the ramifications of these findings for each field and outline some of the outstanding conceptual and mathematical challenges that will likely propel research in the coming years.