The material point method (MPM) has garnered significant attention in recent years owing to its advantages in solving soil–water-structure interaction problems involving large deformations in geotechnical engineering. The MPM combines the benefits of point-based and mesh-based approaches (finite element method) with both Eulerian computational mesh and continuum descriptions of materials. The successful integration of MPM in simulated landslides, internal erosion, and excavation has been frequently reported. However, solving the soil–geosynthetic interaction problem with the MPM has not been explored, although such problems often entail large deformations. The goal of this study is to collate studies on the simulation of geosynthetics and their interactions with soil using MPM. This paper first discusses the basics of MPM and the formation of thin membrane materials using MPM. It also includes limited applications of MPM in simulating soil–geosynthetic interactions. The applications demonstrate that the MPM is particularly effective in resolving large deformation problems associated with geosynthetics, including problems of landfill settlement, reinforced-slope stability, and geocontainer dropping.