International audience Financial market participants and policy-makers can benefit from a better understanding of how shocks can affect volatility over time. This study assesses the impact of structural changes and outliers on volatility persistence of three crude oil markets - Brent, West Texas Intermediate (WTI) and Organization of Petroleum Exporting Countries (OPEC) - between January 2, 1985 and June 17, 2011. We identify outliers using a new semi-parametric test based on conditional heteroscedasticity models. These large shocks can be associated with particular event patterns, such as the invasion of Kuwait by Iraq, the Operation Desert Storm, the Operation Desert Fox, and the Global Financial Crisis as well as OPEC announcements on production reduction or US announcements on crude inventories. We show that outliers can bias (i) the estimates of the parameters of the equation governing volatility dynamics; (ii) the regularity and non-negativity conditions of GARCH-type models (GARCH, IGARCH, FIGARCH and HYGARCH); and (iii) the detection of structural breaks in volatility, and thus the estimation of the persistence of the volatility. Therefore, taking into account the outliers on the volatility modelling process may improve the understanding of volatility in crude oil markets.