This thesis studies currency premia and their connections with macroeconomics. In the first essay, I link currency premia to capital-output ratios and the well-known “Lucas Paradox”. The “Lucas Paradox” states that there are large and persistent differences in capital-output ratios across countries, suggesting capital is not flowing to countries where it is relatively scarce. In the data, capital-output ratios vary a lot cross-sectionally even within developed countries, and they are negatively correlated with currency risk premia and risk-free rates. To rationalize these patterns, I build a quantitative multi-country model of capital accumulation with external habit and heterogeneous exposures to a global productivity shock. I show that currency risk in this model generates cross-country variations in risk-free rates and capital-output ratios that are consistent with the data. I estimate the model using GDP data from countries issuing the G10 currencies and find two main results: (1) The heterogenous loadings that I extract from GDP data alone are highly correlated with capital-output ratios; and (2) when I feed the estimated loadings into the model, model-generated capital-output ratios account for roughly 55% of the cross-country variation in the data. I conclude that variation in currency risk and therefore currency risk premia have significant effects on the real economy. In the second essay, I identify a quantitative puzzle when using canonical consumption-based asset pricing models to match currency premia under complete markets. Canonical long-run risk and habit models induce a strong, negative correlation between the variance and the mean of the log stochastic discount factor to address the well-known equity premium puzzle. When applied to an open economy with complete markets, this key feature requires that differences in currency returns should arise primarily from predictable appreciations, a requirement that is at odds with the data. We term this tension between a high equity premium, smooth risk-free rates, and largely unpredictable exchange rates the currency premium puzzle and argue it is the underlying reason why existing international asset pricing models have struggled to simultaneously match data on currency returns, equity returns, and risk-free rates. In the third essay, I show that perturbation methods lead to significant computational errors when used to solve international risk-sharing models with Epstein and Zin (1989) preferences. In particular, if countries feature different sizes, the simulating results violate law of iterated expectations. Even under symmetric setups, the errors along a typical simulation path are non-negligible. I conclude that perturbation-based solutions of EZ risk-sharing models should be used with caution.