This paper provides an analysis of oil prices during and in the aftermath of the Global Financial Crisis, concentrating on the 2007-08 price spike and the 2014-16 price decline. The mildly explosive/multiple bubbles testing strategy by Phillips, Shi and Yu (2015, International Economic Review 56(4), 1043-1133) is used to test for price departures from an underlying stochastic trend and to assess whether any such departures can be explained by fundamentals or other proxy variables. The test dates two significant time periods in both Brent and WTI nominal and real front-month futures prices: a mildly explosive episode during the 2007-08 spike, prior to the peak of the Global Financial Crisis; and a significantly shorter, negative such episode during the 2014-16 price decline, whose commencement is dated around a key OPEC meeting in November 2014. Evidence using other commodity prices points to explanatory factors beyond commodity markets. A global economic activity proxy is found to be decisive in the episode in mid-2008; excess speculation is not. U.S. shale oil production, though contributing to the post-June 2014 price decline, is not seen to have been decisive. Against some recent work tying the CBOE Volatility Index (VIX) to oil futures prices, we find no evidence that the VIX decisively affected oil price levels during the sample period. The results are compared and contrasted with those obtained by Baumeister and Kilian (2016, Journal of the Association of Environmental and Resource Economists 3, 131-158) via a forecasting approach based on a structural vector autoregressive model without financial variables. Taken altogether, the results herein provide new evidence based on formal statistical testing that help resolve a number of recent controversies in the oil price literature.