We consider two variants of the toll-setting problem in which a traffic authority uses tolls either to maximize revenue or to alleviate bottlenecks in the traffic network. The users of the network are assumed to act according to Wardrop’s user equilibrium so that the overall toll-setting problems are modeled as mathematical problems with equilibrium constraints. We present nonconvex mixed-integer nonlinear reformulations that exploit binary variables and big-M constants for these problems, derive valid big-Ms, prove the existence of optimal solutions, and provide valid inequalities. Moreover, we consider the setting in which the network users hedge against uncertainties in the travel costs. We model this setting using robust Wardrop equilibria under budgeted uncertainty and prove existence of robust solutions. Finally, we present a computational case study to illustrate the effects of considering robustified travel decisions.