Worldwide emphasis on fuel efficiency, low emissions, and use of low-quality fuels such as biogas continues to drive the development of combustors that operate over a wider range of fuel/air ratios and with higher burning velocities than their conventional counterparts. Enhancement of reaction rates is required to increase burning velocities and widen fuel/air operating ranges over values achievable in conventional combustors, and extensive research over the last few decades has shown that transferring heat in a reactor from hot combustion products to incoming reactants can accomplish this enhancement without external energy addition. These reactors, called heat recirculating reactors, use various geometries and flow strategies to optimize the heat transfer. In this paper, research on heat recirculating reactors is reviewed with an emphasis on the most important designs and applications. The basic characteristics of a heat recirculating reactor are encompassed in a simple configuration: a flame stabilized in a tube with high thermal conductivity. More complex designs that have evolved to further optimize heat transfer and recirculation are then described, including porous reactors with or without flame stabilization and channel reactors consisting of parallel tubes or slots. Advanced designs introduce additional means of heat transfer, such as transverse heat transfer from hot products through channel walls to incoming reactants, thereby leading to the counter-flow channel reactor. The flexibility of heat recirculating reactors to operate on a variety of fuels and over wide operating ranges has led to many applications including fuel reformers, radiant heaters and thermal oxidizers, and important work on these applications is reviewed. Finally, future research directions are discussed. (C) 2019 Elsevier Ltd. All rights reserved.