Abstract: The ground penetrating radar (GPR), as a geophysical exploration technique for detecting the distribution of subsurface media based on ultra-high frequency electromagnetic waves, has the advantages of fast detection speed and high resolution, and plays a crucial role in many important fields. Forward numerical simulation occupies a central position in the theoretical research and practical application of ground penetrating radar. It is not only the key to improving the application effectiveness of ground penetrating radar technology, but also an important foundation for the implementation of migration and inversion research, providing powerful support for comprehensive understanding of the propagation mechanism of high-frequency electromagnetic waves and interpreting the complexity of subsurface structures. Firstly, this paper conducts a comprehensive and detailed review of the three main numerical simulation techniques for wave equations, namely, the finite difference time domain method (FDTD), the finite element time domain method (FETD), and the pseudo spectral time domain method (PSTD), in the field of forward numerical simulation of ground penetrating radar. We analyze the advantages and limitations of each of the three methods, and outline the latest technological progress they have achieved in improving the accuracy of numerical simulation and computational efficiency, thus clearly outlining the development context and current situation of these three techniques. Secondly, we analyze and predict the future trends and potential research fields of ground penetrating radar numerical simulation, and provide useful guidance for the further development.