Abstract: Clean and efficient coal utilization becomes an important direction and new research topic under the dual-carbon background. Recently, underground coal gasification (UCG) develops very fast and shows great potential in this area. However, the laboratory and field experiments, which are usually used to investigate the gasification mechanisms and optimize the operating parameters, are quite expensive. Thus, there is a strong demand for the numerical approach that is low-cost, easy operation, and short-cycle. Currently, the numerical approach faces challenges in terms of mathematical modelling and numerical method for solving the nonlinear system because of the complexity of the gasification process. To deal with that, we have done the work as follows: clarified the materials and key problems in each space based on a detailed analysis and revealed the essence of the UCG; summarized four kinds of key mechanical issues including fluid dynamics, thermodynamics, material mechanics, and chemical reaction kinetics; reviewed the development history of numerical research for key mechanical problems in detail and introduced the latest results; illustrated the status of engineering application of numerical research and pointed out the development trends. The work in this paper has positive theoretical significance for the development of the numerical technique for UCG and guiding the design and implementation of UCG trials in China.