Most literature on routing games make the assumption that drivers or vehicles are of the same type and, hence, experience the same latency or cost when traveling along the edges of the network. In contrast, in this article, we propose a heterogeneous routing game in which each driver or vehicle belongs to a certain type. The type determines the cost of traveling along an edge as a function of the flow of all types of drivers or vehicles over that edge. We examine the existence of a Nash equilibrium in this heterogeneous routing game. We study the conditions for which the problem of finding a Nash equilibrium can be posed as a convex optimization problem and is therefore numerically tractable. Numerical simulations are presented to validate the results.