It is customary to suggest that the asymmetry in the transmission of oil price shocks to real output is well established. Much of the empirical work cited as being in support of asymmetry, however, has not directly tested the hypothesis of an asymmetric transmission of oil price innovations. Moreover, many of the papers quantifying these asymmetric responses are based on censored oil price VAR models that have recently been shown to be invalid. Other studies are based on dynamic correlations in the data and do not distinguish between cause and effect. Recently, several new methods of testing and quantifying asymmetric responses of U.S. real economic activity to positive and negative oil price innovations have been developed. We put this literature into perspective, contrast it with more traditional approaches, highlight directions for further research, and reconcile some seemingly conflicting results reported in the literature.