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In this work, we review the routing models that use game theoretical methodologies. A very common assumption in the analysis and development of networking algorithms is the full cooperation of the participating nodes. Most of the analytical tools are based on this assumption. However, the reality may differ considerably. The existence of multiple domains belonging to different authorities or even the selfishness of the nodes themselves could result in a performance that significantly deviates from the expected one. Even though it is known to be extensively used in the fields of economics and biology, game theory has attracted the interest of researchers in the field of communication networking as well. Nowadays, game theory is used for the analysis and modeling of protocols in several layers, routing included. This review aims at providing an elucidation of the terminology and principles behind game theory and the most popular and recent routing models. The examined networks are both the traditional networks where latency is of paramount importance and the emerging ad hoc and sensor networks, where energy is the main concern.