We make three contributions to the volatility impulse response function (VIRF) of Hafner and Herwartz (2006). Firstly, we derive the law of the VIRF in the BEKK model. Secondly, we present a structural embedding of the VIRF by relying on recent developments for identification in MGARCH models. This broadens the use case of the VIRF, to date limited to historical analyses, by allowing for counterfactual and out-of-sample scenario analyses. Thirdly, we show how to endow the VIRF with a causal interpretation. We illustrate the merits of a structural VIRF analysis by investigating the impacts of historical and counterfactual shock events as well as the consequences of well-defined future shock scenarios on the U.S. equity, government bond and foreign exchange market.