We measure funding constraints in international currency markets by deviations in the covered interest rate parity. Our measure of funding risk is the standard deviation of the magnitude of the funding constraints. This funding risk measure appears to be driven by conditions in the financial sector in the low interest rate, so called carry trade short countries, oil price volatility, as well as by the actions of the main central banks. Although funding risk has been present throughout our sample, it becomes only relevant in currency carry trading after 2008, suggesting that investors’ funding constraints start binding at that time. We document evidence that since 2008 funding risk has affected the magnitude of currency carry trading activity, carry trade returns, correlation between carry long and short currencies, relative equity returns in carry trade long vs. short countries, and the economies of carry trade long countries measured through changes in industrial production. We develop a theory of currency markets under funding constraints that has several testable implications. For instance, as funding constraints start to bind, our theory predicts that both the investment and funding currencies drop relative to a safe asset. This result is observable also in our empirical analysis, when we proxy for the safe asset with gold. In line with theory, funding risk forecasts currency crashes in the carry trade long and short countries.