## 1 Introduction
In terms of the ignition process and ignition mechanism, it can be divided into supercritical ignition and transcritical ignition based on existing research results of hydrothermal combustion ignition, based on the supercritical or subcritical state of reactants. Transcritical ignition is a key stage in the process of achieving hydrothermal combustion by feeding cold materials. The ignition mechanism of supercritical ignition and transcritical ignition are slightly different due to the drastic changes of physical properties of the transcritical process, but ignition is generally the result of the interaction of critical physical properties, heat transfer and mixing. [PERSON] et al. studied the difference in the effect of oxidant flow rate (0.5-3 mL/s) on ignition delay time under subcritical (380 \({}^{\circ}\)C, 20.5 MPa) and supercritical (400 \({}^{\circ}\)C, 22.5 MPa) conditions [44]. The disappearance of phase interface and the change of reaction mechanism caused by supercritical pressure and the alterations of reaction mechanism and component transport caused by supercritical water have profoundly changed the ignition mechanism and the ignition process. In practical application, we hope to inject raw materials at room temperature to overcome salt-deposition-caused blockage and preheating-caused high-energy consumption in the SCWO treatment of recalcitrant pollutants. Therefore, it is necessary to study the mechanism of transcritical ignition. Currently, there are only few reviews [14; 36; 45; 46; 47] on the characteristics and improvements of experimental apparatus, the numerical simulation progress, the characteristics of flame and combustion, and especially the ignition process and mechanism, which is not enough for relevant scholars to learn about current research status within limited time. To sort out research outcomes and deficiencies in the existing literature, and to provide useful information for follow-up research, this review was divided into five parts to summarize the literature related to hydrothermal combustion, especially the articles published in the past ten years: (1) Introduction to critical experimental devices (semi-batch reactor and continuous reactor) in different categories according to their institutions. (2) Introduction to the applications of numerical simulation in the field of hydrothermal combustion from the anglesof reaction kinetics and flow-reaction. (3) Summary of research results of supercritical hydrothermal flame and its combustion characteristics by five key factors. (4) Division of the ignition process and explanation of the ignition mechanism from the perspectives of critical physical properties, heat transfer and mixing. (5) Discussion and forecast of the industrial applications from aspects of hydrothermal spallation drilling, thermal recovery of heavy oil, clean conversion and utilization of coal-based fuel and harmless treatment of pollutants. Its skeleton is arranged from experimental equipment to industrial applications, from combustion characteristics to ignition mechanism, and from summary conclusions to prospect prediction. Generally speaking, this review is beneficial for readers to understand the ignition mechanism and the factors affecting flame stability, as well as the design and optimization of HFR, thus promoting its industrial application.