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This article offers a review of the literature on intertemporal stochastic general equilibrium (ISGE) models in an open economy. The basic international ISGEmodel cannot describe the cyclical synchronization ofGDPsobserved in the data, the weak cross-correlation of consumption aggregates, or the sharp swings in the exchange rate.These empirical enigmas have fostered a series of theoretical enhancements to make the models more consistent with the data. The contribution by Obstfeld and Rogoff (1995) is unquestionably a reference model, as it offers a microeconomic foundation for an open-economy Keynesian framework. Recent studies have attempted to go beyond the neo-Keynesian model by incorporating elements from international-trade and portfolio-choice theories.