Since its discovery, the Flameless Combustion (FC) regime has been seen as a promising alternative combustion technique to reduce pollutant emissions of gas turbine engines. This combustion mode is often characterized by well-distributed reaction zones, which can potentially decrease temperature gradients, acoustic oscillations and, consequently NOx emission. However, the application of FC to gas turbines is still not a reality due to the inherent difficulties faced in attaining the regime while meeting all the engine requirements. Over the past years, investigations related to FC have been focused on understanding the fundamentals of this combustion regime, the regime boundaries, its computational modelling, and combustor design attempts. This article reviews the progress achieved so far, discusses the various definitions of the FC regime, and attempts to point the directions for future research. The review suggests that modelling of the FC regime is still not capable of predicting intermediate species and pollutant emissions. Comprehensive experimental databases with conditions relevant to gas turbine combustors are not available, and moreover, many of the current experiments do not necessarily represent the FC regime. By analysing the latest developments in computational modelling, the review points to the most promising approaches for the prediction of reaction zones and pollutant emissions in FC. The lessons learned from previous design attempts provide valuable insights into the design of a successful gas turbine engine operating under the FC regime. The review concludes with some examples where the gas turbine architecture has been exploited to advance the possibilities of FC in gas turbines.