In this study, we analyze the upside and downside risk connectedness among international stock markets. We characterize the connectedness among international stock returns using the Diebold and Yilmaz spillover index approach and compute the upside and downside value-at-risk. We document that the connectedness level of the downside risk is higher than that of the upside risk and stock markets are more sensitive when the stock market declines. We also find that specific periods (e.g., the global financial crisis, the European debt crisis, and the COVID-19 turmoil) intensified the spillover effects across international stock markets. Our results demonstrate that DE, UK, EU, and US acted as net transmitters of dynamic connectedness; however, Japan, China, India, and Hong Kong acted as net receivers of dynamic connectedness during the sample period. These findings provide significant new information to policymakers and market participants.