A definition of super smooth mirror surfaces was given first. On such smooth surfaces the texture as surface roughness is considered to be of the size of surface atoms, provided that there are crystalline terraces but not strain and stress of the damaged layer caused by material processing. Mechanism of material removing in the ultra-precision polishing to reach such a super smooth mirror surface and suitable methods and conditions for the minimization on surface roughness were described, and some examples of such polishing technology were explained: ordinary optical glass surfaces were finished to less than 0.5 nmRy roughness under an improved pitch-polishing. The detail of newly proposed P-MAC (Progressive Mechanical and Chemical) polishing is also described. In this polishing, an abrasive free condition is adopted and the stock removing from work surface accelerated by the chemical reactions accompanying the friction with a closed contact/semi-contact condition between work and polisher surfaces in first step. After removing the ups and downs on surface roughness of work, polishing condition shifts to non-contact condition as second step. By using Br-methanol solution and soft fluorocarbon foam polisher, less than 0.5 nmRy in surface roughness was attained with GaAs wafer surfaces.