This paper investigates the co-movements of oil prices and the exchange rates of 10 top oil-importing and oil-exporting countries. Firstly, we estimated the total static spillover index based on vector autoregressive (VAR) models. Secondly, we adopted the recent DCC-GARCH-CONNECTEDNESS approach proposed by Gabauer (2020) to conduct a time-varying analysis that investigates the directionally dynamic connectedness among WTI and Shanghai crude oil futures and currency markets. We explored contagion spillover volatility by focusing on a sample of major oil-exporting and oil-importing countries using daily data from 4 March 2018 to 25 August 2023. We analysed this relationship during four phases: the entire sample; before COVID-19; during COVID-19; and during the Russian–Ukrainian war. Our results confirm the persistence of volatility for the series studied, thereby justifying the use of the dynamic connectedness approach. Our findings also reveal strong evidence of volatility transmission between oil prices and exchange-rate markets. However, the COVID-19 pandemic and the Russian–Ukrainian war have altered this link. The connectedness between the two markets (petrol and exchange) was stronger at the beginning of the crisis period and then gradually depreciated in value over time. Our findings reveal that exchange rates for both oil-exporting and oil-importing countries are more sensitive to oil price shocks during crises than in normal periods. This suggests that volatility contagion between these two markets continues to exist, thus emphasising the role of oil price shocks as net transmitters across the network during extreme scenarios.