An elastomer is a material that undergoes large deformation under force and quickly recovers its approximate initial shape and size after withdrawing the external force. Furthermore, an elastomer can heal itself and increase volume when in contact with certain liquids. They have been widely used as sealing elements and packers in different oil drilling and development operations. With the development of drilling fluids, elastomer materials have also been gradually used as drilling fluid additives in drilling engineering practices. According to the material type classification, elastomer materials can be divided into polyurethane elastomer, epoxy elastomer, nanocomposite elastomer, rubber elastomer, etc. According to the function classification, elastomers can be divided into self-healing elastomers, expansion elastomers, etc. This paper systematically introduces the research progress of elastomer materials based on material type classification and functional classification. Combined with the requirements for drilling fluid additives in drilling fluid application practice, the application prospects of elastomer materials in drilling fluid plugging, fluid loss reduction, and lubrication are discussed. Oil-absorbing expansion and water-absorbing expansion elastomer materials, such as polyurethane, can be used as lost circulation materials, and enter the downhole to absorb water or absorb oil to expand, forming an overall high-strength elastomer to plug the leakage channel. When graphene/nano-composite material is used as a fluid loss additive, flexibility and elasticity facilitate the elastomer particles to enter the pores of the filter cake under the action of differential pressure, block a part of the larger pores, and thus, reduce the water loss, while it would not greatly change the rheology of drilling fluid. As a lubricating material, elastic graphite can form a protective film on the borehole wall, smooth the borehole wall, behaving like a scaly film, so that the sliding friction between the metal surface of the drill pipe and the casing becomes the sliding friction between the graphite flakes, thereby reducing the friction of the drilling fluid. Self-healing elastomers can be healed after being damaged by external forces, making drilling fluid technology more intelligent. The research and application of elastomer materials in the field of drilling fluid will promote the ability of drilling fluid to cope with complex formation changes, which is of great significance in the engineering development of oil and gas wells.