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In the context of the gradual intensification of the Russia-Ukraine conflict and the continuous spread of the COVID-19 pandemic, this paper concentrates on the impact of global extreme events such as the COVID-19 pandemic and the Russia-Ukraine conflict on the risk spillovers among major international financial markets. First, to measure the impact of the extreme events the on the volatility spillovers among major international financial markets in the time-frequency domain, we combine the TVP-VAR-based connectedness method and BK frequency connectedness approach and focus on the total, directional, and net volatility spillovers. Second, the network visualization method is applied to outline the structural change in the risk contagion, paths, and roles among international financial markets during different periods of global extreme events. The empirical results indicate that the risk spillovers (total, directional, and net spillovers) among international financial markets and the roles played by each market in the process of risk contagion have changed significantly in different periods of global extreme events. Furthermore, volatility spillovers among international financial markets are driven mainly by the high-frequency component (short-term spillovers) during the full sample time. However, the effects of the extreme events also persist in the medium and long terms. Our findings may help understand the dynamics among international financial markets under extreme shocks and provide significant implications for portfolio managers, investors, and government agencies in times of extreme events.