In this study we construct volatility spillover indexes for some of the major stock market indexes in the world. We use a DCC-GARCH framework for modeling the multivariate relationships of volatility among markets. Extending the framework of Diebold and Yilmaz (Int J Forecast 28(1):57–66, 2012) we compute spillover indexes directly from the series of returns considering the time-variant structure of their covariance matrices. Our spillover indexes use daily stock market data of Australia, Canada, China, Germany, Japan, the UK, and the USA, for the period April 1996–June 2017. We obtain several relevant results. First, total spillovers exhibit substantial time series variation, being higher in moments of market turbulence. Second, the net position of each country (transmitter or receiver) does not change during the sample period. However, their intensities exhibit important time variation. Finally, transmission originates in the most developed markets, as expected. Of special relevance, even though the Chinese stock market has grown importantly over time, it is still a net receiver of volatility spillovers. However, the magnitude of net volatility reception has decreased over the last few years.