Electrical discharge machining is one of the important non-conventional machining operations in modern engineering field. Electrical discharge machined components are extensively used in various areas such as automobile, aerospace, medical, etc. The materials having high strength, hardness and wear resistance are effectively machined. The high accuracy and precision of electric discharge machines make it an important machining operation in the modern world. There are several modifications and process improvement techniques in this area to enhance the performance of electrical discharge machining. The process parameters, selection of dielectric medium and tool electrodes are important aspects of electrical discharge machining that determine the performance parameters such as MRR, TWR and surface integrity. There are various types of EDM based on the selection of dielectric medium. They are wet EDM, dry EDM, Powder mixed EDM and near-dry EDM. This literature review is classifying the EDM based on different dielectric medium and numerical modeling works on EDM are investigated. Numerical modeling using finite element method is focused in this paper. The process parameters which influence the modeling of EDM are also studied. It is found that near-dry EDM which use mixture of liquid and gas as the dielectric medium have superior performance characteristics compared with conventional EDM practices. There are few studies are carried out on the numerical modeling of near-dry EDM and further studies are to be carried out to optimize the performance of EDM. This paper aims to provide a review on different dielectric medium used in EDM and numerical modeling of electrical discharge machining by finite element method.