This article unveils the dependence structure between crude oil prices, exchange rates, and the United States interest rates. We begin by using asymmetric GARCH models to examine the marginal behavior of the returns, and then various copulas are used to understand extreme market co-movements. We also investigate the causal relationship and the spillover effects by using the Granger causality test and the BEKK representation of a multivariate GARCH process. Over the 1998-2017 period, we find evidence of an inverse relationship between the U.S. interest rates and the crude oil prices. Oil-exchange rate linkages become stronger for most of the oil dependent countries considered in this article in the aftermath of the global financial crisis. There is also asymmetric tail dependence for almost all of the oil-exchange rate pairs. The results of Granger causality tests mainly indicate that crude oil prices Granger cause exchange rates. We also find that there are unidirectional volatility spillovers from
WTI to exchange rates for oil exporting countries and to the U.S. interest rates. These findings provide important implications for investors to hedge the possible risk with international portfolio diversification.