A review of turbine-burner research and a discussion of some relevant background issues for this emerging technology are presented. The thermal cycle analysis for augmentative combustion in the passages of the turbine on a turbojet or turbofan engine is discussed, identifying the potential for dramatic improvements in engine performance. The substantial challenges of augmentative combustion integrated with the turbine function are outlined, including the need for flame stabilization in accelerating flows at the 10 5 g levels. Research findings on reacting mixing layers in accelerating flows and flameholding in high-speed flows are reviewed. Descriptions are given of various types of compact combustors which can be used as main combustors or augmentative combustors between turbine stages. An overview is given of recent computational research at UCI on the stabilization of flames in accelerating and turning flows. Two-dimensional computations for Reynolds-averaged turbulent flow through straight and turning channels are discussed. Quasi-two-dimensional representations of reacting, converging (and converging/ turning) channel flows are examined. Two-and three-dimensional computations for time-dependent transitional flows through passages are given for cases with and without cavities. Rossiter modes, found only for the non-reacting cases, are discussed. Various configurations for injection of fuel and air into the cavity are examined. Cavity placements on the inside and outside of the turn are studied to provide different centrifugal accelerations. Some indications for optimizing the cavity design are presented. Effects of the cavity length and depth, injection orientation for fuel and air into the cavity, passage turning radius, and Reynolds number magnitude are discussed. Various hydrodynamic instabilities associated with mixing and combustion in accelerating, turning flows are evaluated, and the needs for future work are identified.