A polishing apparatus is used for polishing a substrate such as a semiconductor wafer, and has a sensor capable of continuously detecting the thickness of an electrically conductive layer. The polishing apparatus includes a polishing table having a polishing surface, and a top ring for holding and pressing the substrate against the polishing surface to polish the surface of the substrate. A sensor such as an eddy-current sensor is disposed below the polishing surface of the polishing table for measuring the thickness of a conductive layer formed on the surface of the substrate.