Cognitive effort has long been an important explanatory factor in the study of human behavior in health and disease. Yet, the biophysical nature of cognitive effort remains far from understood. In this talk, I will offer a network perspective on cognitive effort. I will begin by canvassing a recent perspective that casts cognitive effort in the framework of network control theory, developed and frequently used in systems engineering. The theory describes how much energy is required to move the brain from one activity state to another, when activity is constrained to pass along physical pathways in a connectome. I will then turn to empirical studies that link this theoretical notion of energy with cognitive effort in a behaviorally demanding task, and with a metabolic notion of energy as accessible to FDG-PET imaging. Finally, I will ask how this structurally-constrained activity flow can provide us with insights about the brain’s non-equilibrium nature. Using a general tool for quantifying entropy production in macroscopic systems, I will provide evidence to suggest that states of marked cognitive effort are also states of greater entropy production. Collectively, the work I discuss offers a complementary view of cognitive effort as a dynamical process occurring atop a complex network.