In this paper we survey the recent literature on long run, or equilibrium, exchange rate modeling. In particular, we review the voluminous literature which tests for a unit root in real exchange rates and the closely related work on testing for a unit root in the residual from a regression of the nominal exchange rate on relative prices. We argue that the balance of evidence is supportive of the existence of some form of long-run exchange rate relationship. The form of this relationship, however, does not accord exactly with a traditional representation of the long-run exchange rate. We offer some potential explanations for this lack of conformity.