Rotating detonation combustors (RDC) are at the forefront of pressure gain combustion (PGC) research, utilizing one or more azimuthally spinning detonation waves, an intrinsically unsteady process, to effect a stagnation pressure rise across the device. The prospective step-increase in efficiency, simplicity of design without the requirement for mechanical actuations and the ease of assembly make it an especially promising technology that could be integrated into existing propulsion and power generation architectures. This is coupled with the significant complexity of the detonation-based multi-axis flow field and the associated combustion modes and coupling mechanisms. The current paper is an overview of the research done worldwide to address some of the challenges and questions pertaining to the physics of RDC operation. When appropriate, notable parallels are drawn to the phenomena of low and high frequency instabilities in solid and liquid rockets that have been recognized as the most severe hindrance to their operation. (C) 2019 Elsevier Ltd. All rights reserved.