Roughness down to atomic and close-to-atomic scale is receiving an increasing attention in recent studies of manufacturing development, which can be realized by high-precision polishing processes. This review presents polishing approaches at atomic and close-to-atomic scale on planar and curved surfaces, including chemical mechanical polishing, plasma-assisted polishing, catalyst-referred etching, bonnet polishing, elastic emission machining, ion beam figuring, magnetorheological finishing, and fluid jet polishing. These polishing approaches are discussed in detail in terms of removal mechanisms, polishing systems, and industrial applications. The authors also offer perspectives for future studies to address existing and potential challenges and promote technological progress.