This paper uses a structural vector autoregression model to investigate the inflationary effects of oil prices. Rather than simply infer the oil price changes as oil supply shocks, we identify three different shocks in the crude oil market: the oil supply shock, the global aggregate demand shock, and the oil-market specific demand shock. We then use impulse response functions to compute the conditional oil price pass-through ratios. It is found that the largest oil price pass-through is caused by oil supply shocks. However, evidence from historical decompositions suggests that the oil price movements have been driven by shocks from strong global aggregate demand and oil demand while only minor contributions come from oil supply shocks. Disentangling demand and supply shocks in the crude oil market helps to uncover the fact that a recent decline in unconditional oil price pass-through may come from the low conditional pass through caused by global demand shocks.