Methods and apparatus for finishing an edge of a glass sheet are described. The edge of the glass sheet is finished using a grinding wheel mounted on one end of a spindle, the grinding wheel having a peripheral edge that contacts the edge of the glass sheet during the grinding. The edge of the glass sheet is further finished by polishing the edge of the glass sheet with a polishing wheel mounted on one end of a spindle, the polishing wheel having an end face which contacts the glass edge during polishing.