We first utilized the Bayes positive diagonal BEKK generalized autoregressive conditional heteroskedasticity (Bayes-pdBEKK-GARCH) model to evaluate the risk spillovers between the e-commerce and logistics, then applied the adaptive Fourier decomposition method to measure the extent of these spillovers and detect structural changes. The results showed that there were structural breaks in both markets, which may lead to extreme risks. At last, we applied the GARCH-copula quantile regression model to analyze the extreme risks. We found that: (1) there were asymmetric volatility spillovers and positive correlations between them. (2) The dynamic risk spillovers exhibited heterogeneity over time. The logistics market had a smaller downside risk spillover, while the e-commerce market had a stronger upside risk spillover. (3) The study indicated that important events, such as the Chinese stock market crash, the Sino-U.S. trade friction, the COVID-19 epidemic, and the "either-or choice" monopoly policy of e-commerce platforms, had a significant influence on them, resulting in dramatic risk spillovers.