Nonconventional machining technologies have been found viable to manufacture various products from a wide range of engineering materials. Wire electric discharge machining (WEDM), also known as Wire-EDM, is one of the important thermal type nonconventional machining technologies. Wire-EDM is being preferably used by manufacturers to produce biomedical devices including bio and dental implants. This paper presents an overview of capabilities of wire-EDM type nonconventional machining technology for the precise machining of titanium and its alloys for biomedical applications. It reviews the important research work conducted on machining titanium alloys by wire electrical discharge machining (WEDM). Their findings and achievements are discussed to encourage further research and development in the biomaterial machining area.