In electrical discharge machining (EDM), material removal is caused by electrical discharges that take place between the tool electrode and the workpiece electrode. Thermal mechanisms dominate the removal process. In the case of metals, for example, material layers are strongly heated, melt and vaporize. However, other removal mechanisms are also known, such as spalling due to thermal shock in electrically conductive ceramics. After the discharge is complete, a characteristic surface topography and a multi-layered surface rim zone remain on the workpiece. The constitution of this rim zone is decisive for the functionality of the component. After introduction of the physical principles, extensive descriptions of the technology as well as the process and tool design are given. The focus is on how the electrical discharge machining process can be influenced by the generator settings, the dielectrics, the flushing conditions and the electrode materials. The setting up of models, control strategies and possibilities for process monitoring are also addressed. The chapter concludes with examples of the practical application of electrical discharge machining and wire EDM and shows how special manufacturing tasks can be solved using customized processes.