This paper analyzes the volatility spillovers across global financial markets using a generalized variance decomposition, and by incorporating a fast-tractable Markov regime-switching framework into the vector autoregressive (VAR) model. The new approach outperforms the classical single-regime framework, by detecting different dynamics of spillovers during periods of crisis and periods of tranquility. Moreover, the proposed estimation method has the advantage over existing procedures to converge remarkably fast when applied to a large number of variables. Empirical investigation on volatility indices of eight developed financial stock markets shows that the total and directional spillovers are more intense during turbulent periods, with frequent swings between net risk transmission and net risk reception. Conversely, during periods of tranquility, volatility spillovers are relatively moderate.