Wire Electrochemical Micromachining (Wire ECMM) process has become a topical field of research in today's context of micromachining. This is due to the agility which the process offers, that makes it as one of the most suitable option for machining of micro parts and features. Process capabilities of the Wire ECMM such as protracted tool life, surface integrity, material removal rate, surface finish, burr and heat affected zone-free surface gives it an edge over Wire Electric Discharge Machining (WEDM), its counterpart in thermal based machining process. However, the control of process parameters in Wire ECMM is not easy and requires knowledge of their influence. At present, Wire ECMM is still a lab-based technique. This article aims to provide a detailed and well-arranged literature survey of the advancements made in Wire ECMM to date along with an insightful discussion on the science of electrochemical dissolution. Key factors influencing the process performance are identified and reviewed. Different analytical and numerical models proposed in the process are also reviewed critically. This article is expected to assist the researchers/practicing engineers in identifying the existing research gaps and contributing towards making Wire ECMM an industrially viable option for micromachining.