The wire cut EDM is one of the most important machining process for technologists in the field of moulds, dies and in precision manufacturing .The wire electrical discharge machining producing parts with in very short period , the demand over the time increases extensively .So that an extensive research work has been carried out to optimize the parameters of the process by eliminating trial and error cost for the selection of parameters during machining of materials, for getting optimum responses like best surface finish, metal removal rate, with good dimensional accuracy and with retaining the physical and chemical properties of parent material. The present paper mainly explores the review of the research work carried out by various research workers with various methodologies and how the output parameters of the WEDM like surface finish , metal removal rate, dimensional accuracy and HAZ were affected by the input process parameters like on time, off time, voltage, wire tension, wire feed, dielectric pressure. current, etc.