Theoretical research on premixed turbulent reactants impinging on a nearby wall is reviewed. The virtues of these flows for fundamental studies and the significant possibilities of flows not studied to date are discussed. An asymptotic analysis which exploits the small magnitude of two parameters arising in the describing equations is outlined and shown to expose the main features of these flows. If the mean density distribution is taken from experiment, the analysis is shown to yield results in excellent agreement with data for the mean axial velocity from a variety of experiments and with the only available second moment data. The problem of predicting the mean density distribution is discussed.