This invention provides a membrane-mediated electropolishing apparatus for polishing and/or planarizing metal work-pieces. The work-piece is wetted with a low-conductivity fluid. The wetted work-piece is contacted with a first side of a charge-selective ion-conducting membrane, wherein the second side contacts a conductive electrolyte solution in electrical contact with a electrode. Current flow between the electrode and the work-piece electropolishes metal from the work-piece. This invention also provides a half-cell adapted for use in membrane-mediated electropolishing having a fully or partially enclosed volume, a conductive electrolyte which partially or essentially fills the enclosed volume, an electrode which is in contact with the electrolyte, and a charge-selective ion-conducting membrane which seals one surface of the enclosed volume, cavity or vessel in such a way that the internal surface of said membrane contacts the electrolyte solution or gel and the external surface is accessible to contact the work-piece.