The exponential growth of computing power in the last two decades opens up entirely new options for numerical simulations of the Electric Arc Furnace (EAF). Simulations can be used to analyze physical phenomena resisting direct observation or operational measurement even to this very day. This paper gives an overview of the state‐of‐the‐art of the Computational Fluid Dynamics (CFD) simulation on the EAF as well as an outlook on future fields of application, while being well aware that by far not all phenomena and literature can be used. The paper makes no claim to exhaustiveness, especially since three subjects of simulation technology have to be excluded: Process models for furnace controlling, stress calculations, electromagnetic simulations. Thus, the focus is on the fluid‐ and thermo‐dynamic furnace processes and on fundamental methods that can be applied to examine these processes. The basic EAF functionalities and selected fluid‐dynamic simulations are presented, for example, on multiphase flow, thermal loading of refractory lining and wall panels, chemical reactions and post‐combustion, oxygen injection technology, and bottom tapping.