The real exchange rate (RER) measures relative price levels across countries, capturing deviations from purchasing power parity (PPP). RER is a key variable in international macroeconomic models as it is central to equilibrium conditions in both goods and asset markets. It is also one of the most starkly behaving variables empirically, tightly comoving with the nominal exchange rate and virtually uncorrelated with most other macroeconomic variables, nominal or real. This review lays out an equilibrium framework of RER determination, focusing separately on each building block and discussing corresponding empirical evidence. We emphasize home bias and incomplete pass-through into prices with expenditure switching and goods market clearing, imperfect international risk sharing, country budget constraint, and monetary policy regime. We show that RER is inherently a general equilibrium variable that depends on the full model structure and policy regime, and therefore partial theories like PPP are insufficient to explain it. We also discuss issues of stationarity and predictability of exchange rates.