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 asymmetries, 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 which recently have been shown to be invalid. Other studies are based on dynamic correlations in the data that do not shed light on the central question of whether the structural responses of real output triggered by positive and negative oil price innovations are asymmetric. Recently, a number of new methodologies have been introduced and applied to the problem of testing and quantifying asymmetric responses of U.S. real economic activity to positive and negative oil price innovations. Our objective is to put this literature in perspective, to contrast it with more traditional approaches, to highlight directions for further research, and to reconcile some seemingly conflicting results reported in the literature.