The present invention relates to a polishing method and a polishing apparatus for polishing a substrate, such as a wafer. This method includes: polishing a substrate W; producing a torque waveform while polishing the substrate W; and selecting one reference torque waveform from a plurality of reference torque waveforms accumulated before the polishing of the substrate W. Polishing the substrate W includes an asperity polishing process and a flat polishing process. The asperity polishing process includes: determining film thicknesses at measurements point on the substrate W based on a film thickness of reference film data calculated based on a first relational expression; comparing the torque waveform and the selected reference torque waveform; and determining whether the asperity polishing process should be terminated. The flat polishing process includes determining film thicknesses at measurement points on the substrate W based on a film thickness of reference film data calculated based on a second relational expression.