The last five decades have witnessed dramatic changes in crude oil price dynamics. We identify the influence of extreme oil shocks and changing oil price uncertainty dynamics associated with economic and political events. Neglecting these features of the data can lead to model misspecification that gives rise to: firstly, an explosive volatility process for oil price uncertainty, and secondly, erroneous output growth dynamic responses to oil shocks. Unlike past studies, our results show that the sharp increase in oil price uncertainty after mid-1985 has a pernicious effect on output growth. There is evidence that output growth responds symmetrically (asymmetrically) to positive and negative shocks in the period when oil price uncertainty is lower (higher) and more (less) persistent before (after) mid-1985. These results highlight the importance of accounting for outliers and volatility breaks in oil price and output growth and the need to better understand the response of economic activity to oil shocks in the presence of oil price uncertainty. Our results remain qualitatively unchanged with the use of real oil price.