•The forex market exhibits asymmetric volatility connectedness.•We use high-frequency data of the most actively traded currencies over 2007–2015.•We document that the negative spillovers dominate positive spillovers.•Positive spillovers are correlated with the subprime crisis.•Negative spillovers are chiefly tied to the dragging sovereign debt crisis in Europe. We show how bad and good volatility propagate through the forex market, i.e., we provide evidence for asymmetric volatility connectedness on the forex market. Using high-frequency, intra-day data of the most actively traded currencies over 2007–2015 we document the dominating asymmetries in spillovers that are due to bad, rather than good, volatility. We also show that negative spillovers are chiefly tied to the dragging sovereign debt crisis in Europe while positive spillovers are correlated with the subprime crisis, different monetary policies among key world central banks, and developments on commodities markets. It seems that a combination of monetary and real-economy events is behind the positive asymmetries in volatility spillovers, while fiscal factors are linked with negative spillovers.