This paper reviews the state of art on microscopic/mesoscopic numerical simulation and macroscopic numerical simulation for the shock initiation process of heterogeneous explosives, summarizes the development trends of numerical simulation of shock initiation in heterogeneous explosives, and enables readers to have a deeper understanding of numerical simulation methods and the mechanism of shock initiation. Both the microscopic and mesoscopic methods have their own limitations, therefore, it is necessary to develop a new computational framework that can capture various mechanisms in the shock initiation process while considering boundary identification, large deformation calculation, and computational efficiency. Hot spots in heterogeneous explosives can be classified into defect-induced and defect-free hot spots based on the presence of structural defects, and both types of hotspots exhibit energy localization effects under shock. The coupling mechanisms between different types of hotspots under shock are not yet clear, and it is necessary to conduct research on the coupling interactions among various types and scales of hotspots to comprehensively reveal the mechanism of hotspots in shock initiation, thereby providing support for numerical simulations of various stages of shock initiation. The physical mechanisms considered in the existing macroscopic reaction rate models for shock initiation are not comprehensive and have weak universality. It is necessary to develop models that account for the coupled effects of multiple hotspots and their statistical distributions which will enhance the universality and predictive capability of macroscope simulation. In the simulation of the entire shock initiation process, macro simulation may overlook many details, while micro/meso numerical simulation requires huge computational complexity. Consequently, it is essential to combine the advantages of both methods to develop multiscale simulation methods to reduce computational consumption and introduce some necessary microscopic information in macro simulation.