Various methods have been proposed to ensure the serviceability of buried structures such as road tunnels, urban utility tunnels, water conduits, underground shelters, and deposition chambers against extreme loads, the most common of which are experimental and computational methods. An external explosion in the vicinity of such structures is one of these extreme loads. In general, different types of external blasting for buried structures can be classified as surface blasting, coupled or uncoupled buried explosions, excavation by drilling and blasting near the structure, and the accidental detonation of explosive depositions. Laboratory or field tests for explosions are usually limited by financial and safety constraints; therefore, numerical simulations are often regarded as a vital tool in the study of such problems. Though computer software and hardware have improved rapidly in recent decades, and various numerical solvers have been developed, there is no universal method for solving all external explosion problems. Each numerical method can produce sensible results under certain conditions and assumptions, along with its limitations in computational cost. Consequently, these problems have been particularly difficult to investigate, and even in some cases, the results of different studies seem to be inconsistent. Besides providing an extensive review of the available literature in the field of numerical simulation of external explosions near buried structures and a discussion of the damage criteria associated with such explosions, this study also highlights some inconsistencies that may need further investigation.