A machine for machining optical workpieces, in particular plastic spectacle lenses, which has a workpiece spindle, which drives the workpiece in rotation about a workpiece rotation axis (B), and a fast tool arrangement, which moves a turning tool in a fast tool movement plane (X-F1), wherein the workpiece spindle and the fast tool arrangement can moreover be moved relative to one another in a plane (X-Y) which contains the workpiece rotation axis (B). The fast tool movement plane (X-F1) is positioned obliquely (work angle α) with respect to the plane (X-Y) containing the workpiece rotation axis (B). As a result, a machine is provided in which the working point of the cutting edge of the turning tool can be aligned in a particularly simple and highly precise manner on the rotation axis (B) of the workpiece spindle.