Abstract: Oblique detonation utilizes shock waves to achieve self-pressurized combustion in supersonic flow, enabling high-efficiency and rapid conversion of chemical energy into mechanical energy. Employing oblique detonation as the core mode for combustion organization, oblique detonation engine offers advantages such as high specific impulse, wide operable Mach number range, and compact structure, making it a highly promising solution for air-breathing high-Mach-number propulsion systems. However, the key challenges of this type of engine lie in the reliable initiation and sustained stabilization of oblique detonation waves. Due to spatial confinement of flow path in the engine combustor, the oblique detonation phenomenon exhibits different initiation and stabilization characteristics from those in conventional unconfined spaces. For example, the limited flow path length may fail to meet the streamwise distance required for oblique detonation wave initiation, leading to failed initiation or insufficient combustion. Additionally, flow constraint in the transverse directions by the combustor walls may cause destabilization and upstream propagation of oblique detonation waves, violating the normal operation of engines. Therefore, in-depth research on the initiation and stabilization characteristics, flow mechanisms, and corresponding flow control methods of oblique detonation waves under space-confined conditions is of great importance to advance the applications of oblique detonation technology in propulsion systems. This paper aims to review the research progress on both the initiation and stabilization of oblique detonation waves in confined spaces, thereby providing insights for future research on oblique detonation engines regarding these two aspects.