A polishing apparatus polishes a periphery of a substrate by bringing a polishing tool into sliding contact with the substrate. The polishing apparatus includes a substrate-holding mechanism configured to hold a substrate and rotate the substrate, a polishing mechanism configured to press a polishing tool against a periphery of the substrate so as to polish the periphery, and a periphery-supporting mechanism configured to support the periphery of the substrate by a fluid. The periphery-supporting mechanism is configured to support a surface of the substrate from an opposite side or the same side of the periphery of the substrate.