Polishing device for polishing curved lens faces of optical lenses, - wherein the polishing device has a workpiece holder for receiving an optical lens and a polishing tool, - wherein the polishing tool having a curved polishing face is driven in a rotating manner about a rotation axis, - wherein either the curved lens face is concave and the curved polishing face is convex or the curved lens face is convex and the curved polishing face is concave, - wherein the workpiece holder is rotatably driven about a first axis in order to rotate about the optical lens, - wherein a spacing (z) can be adjusted between the workpiece holder and the polishing tool along a second axis, - wherein an offset (x) between the workpiece holder and the polishing tool can be adjusted along a third axis which is orientated transversely relative to the first axis, - wherein an angle of attack between the rotation axis and the first axis can be adjusted by means of tilting about a fourth axis, characterised in that - the polishing tool has a carrier element and a resilient substructure, wherein the curved polishing face is arranged on the resilient substructure, and, - when an optical lens is received in the workpiece holder, the polishing tool can be placed in accordance with the angle of attack in an oblique manner on the curved lens face and, by means of deformation of the resilient substructure, a strip-like contact face can be formed between the polishing face and the curved lens face, - wherein the angle of attack between the rotation axis and the first axis is so large that the polishing face is partially raised from the curved lens face and a portion of the polishing face floats in a state laterally spaced apart from the contact face above the lens face. - wherein the polishing device has a workpiece holder for receiving an optical lens and a polishing tool, - wherein the polishing tool having a curved polishing face is driven in a rotating manner about a rotation axis, - wherein either the curved lens face is concave and the curved polishing face is convex or the curved lens face is convex and the curved polishing face is concave, - wherein the workpiece holder is rotatably driven about a first axis in order to rotate about the optical lens, - wherein a spacing (z) can be adjusted between the workpiece holder and the polishing tool along a second axis, - wherein an offset (x) between the workpiece holder and the polishing tool can be adjusted along a third axis which is orientated transversely relative to the first axis, - wherein an angle of attack between the rotation axis and the first axis can be adjusted by means of tilting about a fourth axis, - the polishing tool has a carrier element and a resilient substructure, wherein the curved polishing face is arranged on the resilient substructure, and, - when an optical lens is received in the workpiece holder, the polishing tool can be placed in accordance with the angle of attack in an oblique manner on the curved lens face and, by means of deformation of the resilient substructure, a strip-like contact face can be formed between the polishing face and the curved lens face, - wherein the angle of attack between the rotation axis and the first axis is so large that the polishing face is partially raised from the curved lens face and a portion of the polishing face floats in a state laterally spaced apart from the contact face above the lens face.