We study connectedness and causality between oil prices and exchange rates dynamically. Using data on the WTI and exchange rate returns for six countries in which oil production is a major production activity, we show that oil prices are net receptors of spillovers from excahnge rate markets. Connectedness exhibits important time variation and presents a positive trend during our sample period. We find evidence of bidirectional causality between oil prices and exchange rates, which presents also considerable time-variation. Causality is identified for longer periods of time from oil prices to exchange rates. However, we also find evidence of reverse causality, mainly in the period after the Subprime Financial Crisis. Our results provide evidence supporting the hypothesis of the financialization of oil markets.