The principles of applying electrical discharge in die-sinking and wire-cutting machines are reviewed. This technique causes material to be eroded by switching electrical current on and off between the tool and the work-piece through a dielectric fluid. For the case of metals and many ceramics and ceramic composites, the mechanism for this erosion is melting or perhaps evaporation/condensation. For refractory materials, a new mechanism for erosion, thermal spalling, was observed. The role of the dielectric fluid, its purity, and the proper nitration system are discussed. The effect of various operating conditions, including the current, pulse time duration, and wire feed rate, on the material removal rate and the surface quality is also reviewed. It was seen that EDM can be applied to machining advanced materials, including single phases and composites of ceramic/ceramic and ceramic/metal, if a minimum electrical conductivity is met.