Abstract: The ghost fluid method (GFM) provides a simple way to simulate multi-medium flows with immiscible interfaces. Especially, the modified ghost fluid method (MGFM) and its variants, based on multi-medium Riemann problem solvers, are capable of faithfully taking into account the effects of nonlinear wave interaction and material property at the interface. These treatments have been shown to be efficient when applied to solve various challenging problems involving large discontinuities at the material interface. The MGFM and its variants, therefore, have great potential in engineering applications. In this paper, the development of such method was reviewed. The methodologies of representative GFM-based algorithms for definition of interface conditions and extension to multi-dimensions were compared to each other. The research progresses in design principle and accuracy analysis were also briefly described. In addition, some other typical applications in more challenging scientific problems were presented. Such advantages and features built in the GFM-based algorithms were also summarized.