Abstract: The invention relates to a device (100) for the grinding and/or polishing of planar surfaces, comprising a grinding and/or polishing tool (20), a frame (40), a workpiece (32) or a holder (30) for at least one workpiece, and a means (10) for moving the frame and the workpiece holder (30) with the workpiece, characterized in that the device (100) is set up in such a way that a loose bearing is formed between the workpiece (32) or the workpiece holder (30) and the frame (40), and the means (10) for moving the frame (40) and the workpiece (32) or the workpiece holder (30, 30?) with the at least one workpiece (32) is configured in such a way that the workpiece (32) or the workpiece holder (30) with the at least one workpiece (32) is guided in a plane which is predetermined by the surfaces of the at least one workpiece (32) resting on the grinding and/or polishing tool (20). The invention also relates to a method for the polishing of planar optics by using the device (100).