A polishing apparatus includes a stage configured to hold a substrate, a stage-rotating mechanism configured to rotate the stage, and a polishing head configured to polish a periphery of the substrate held by the stage. The polishing apparatus also includes a controller configured to control operations of the stage, the stage-rotating mechanism, and the polishing head, an image-capturing device configured to capture an image of the periphery of the substrate through at least one terminal imaging element arranged so as to face the periphery of the substrate, an image processor configured to process the image captured by the image-capturing device, and a liquid ejector configured to eject a light-transmissive liquid toward the periphery of the substrate to fill a space between the periphery of the substrate and the terminal imaging element with the liquid.