Electric vehicle routing problems (E-VRPs) extend classical routing problems to consider the limited driving range of electric vehicles. In general, this limitation is overcome by introducing planned detours to battery charging stations. Most existing E-VRP models assume that the battery-charge level is a linear function of the charging time, but in reality the function is nonlinear. In this paper we extend current E-VRP models to consider nonlinear charging functions. We propose a hybrid metaheuristic that combines simple components from the literature and components specifically designed for this problem. To assess the importance of nonlinear charging functions, we present a computational study comparing our assumptions with those commonly made in the literature. Our results suggest that neglecting nonlinear charging may lead to infeasible or overly expensive solutions. Furthermore, to test our hybrid metaheuristic we propose a new 120-instance testbed. The results show that our method performs well on these instances.