We survey the empirical literature on floating nominal exchange rates over the past decade. Exchange rates are difficult to forecast at short- to medium-term horizons. There is a bit of explanatory power to monetary models such as the Dornbusch "overshooting" theory, in the form of reaction to "news" and in forecasts at long-run horizons. Nevertheless, at short horizons, a driftless random walk characterizes exchange rates better than standard models based on observable macroeconomic fundamentals. Unexplained large shocks to floating rates must then, logically, be due either to innovations in unobservable fundamentals, or to non-fundamental factors such as speculative bubbles. The observed difference in exchange rate and macroeconomic volatility under different nominal exchange rate regimes makes us skeptical of the first view. The theory and evidence on speculative bubbles, however, is not conclusive. We conclude with the hope that promising new studies of the microstructure of the foreign exchange market might eventually rise to insights into these phenomena.