This paper employs the Quantile Autoregressive Distributed Lags (QARDL) model developed recently by Cho et al. (2015) to investigate the pass-through of oil prices to a set of energy prices. This approach allows analyzing simultaneously short-term connections and long-run cointegrating relationships across a range of quantiles. It also provides insights on the short-run predictive power of oil prices in predicting energy prices while accounting for the cointegration between oil prices and each of the considered energy prices in low, medium and high quantiles. Two key findings emerge from this paper. First, all considered energy prices are shown to be cointegrated with oil price across quantiles meaning that a stationary equilibrium relationship exists between single energy price and oil price. Second, we find evidence that oil price is a significant predictor of individual petroleum products prices and natural gas in the short run. This paper has important policy implications for forecasters, energy policy-makers and portfolio managers.