A polishing method polishes and planarizes a substrate. The substrate is pressed against a polishing surface on a rotating polishing table. During polishing, the polishing table is rotated, and the surface, being polished, of the substrate is scanned by an eddy current sensor provided in the polishing table. An output of the eddy current sensor is monitored, and substrate damage is detected from a change in the output of the eddy current sensor. Further, an output of an end point detecting sensor obtained by scanning the surface of the substrate is monitored, and the polishing end point is detected from a change in the output of the end point detecting sensor. After detecting the polishing end point, an output of the end point detecting sensor or another sensor is monitored, and detecting a film left on a part of the substrate is performed.