Magnetorheological finishing (MRF®), as a leading-edge production technology, is widely utilized in the optics industry for manufacturing modern optical elements for such applications as advanced lithography used in manufacturing of integrated circuits with nanometre features, lasers, airborne surveillance, weapon systems, medical devices, digital photography, mirrors for space telescopes etc. In this chapter, a relatively brief description of MRF is followed with detailed considerations of scientific aspects of this technology. In this regard, two different approaches are considered for modeling of the mechanism of material removal in MRF. The model of an elastic pad formed from MR fluid in a magnetic field appeared to be unsound in view of the measurements and analysis of mechanical properties of such material. It was shown that an analog of a conventional pad formed with magnetized MR fluid cannot support an abrasive particle load, which would be appropriate to provide removal rates typical for MRF. An alternative approach is based on the principle of conservation of particles momentum in a binary suspension and suggests that a load for surface nano-indentation by abrasive particles is provided at their interaction near the wall with larger and heavier basic magnetic particles fluctuating due to collision in the shear flow of concentrated slurry. Regularity of the granular shear flow and numerical simulation are used in modeling. The model is in good qualitative and reasonable quantitative agreement with experimental results for MRF. The presented results of finishing of some challenging surfaces demonstrate the efficiency of the technology.