This paper provides a selective overview of nonlinear exchange rate models recently proposed in the literature and assesses their contribution to understanding exchange rate behavior. Two key questions are examined. The first question is whether nonlinear autoregressive models of real exchange rates help resolve the "purchasing power parity (PPP) puzzles." The second question is whether recently developed nonlinear, regime-switching vector equilibrium correction models of the nominal exchange rate can beat a random walk model, the standard benchmark in the exchange rate literature, in terms of out-of-sample forecasting performance. Finally, issues related to the adequateness of standard methods of evaluation of (linear and nonlinear) exchange rate models are discussed with reference to different forecast accuracy criteria.