Elastic Emission Machining (EEM) is an advanced ultra-smooth surface manufacturing technology that achieves the machining in the accuracy of the atomic size. By utilizing elastic contact between polishing particle and the workpiece surface, chemical bond form at the interface, enabling the chemical removal of surface atoms. This process can avoid efficiently surface defects and subsurface damage, and EEM is widely applied in many fields such as lithography and synchrotron radiation for fabricating ultra-smooth optical components. This chapter systematically introduces material removal mechanism, slurry driving methods, equipment development, and process optimization. It elaborates on the chemical reactions between particle and the workpiece, their impact on surface morphology, and the effects of fluid dynamics and particle motion. Two main slurry driving methods are discussed, along with strategies to enhance surface quality and removal rate. The evolution of EEM equipment and polishing tools is reviewed, highlighting performance improvements. Finally, the chapter summarizes EEM applications in high-performance optics and proposes future research directions. It is expected that this chapter can provide valuable reference and enlightenment for the development of ultra-precision machining technology.