A machine tool having a material-removing cutting tool, consisting of a carrier which carries at least one cutting element, wherein the cutting tool is mounted in a tool holder or bearing of the machine tool, and the machine tool is equipped with a device for controlling the machining of workpieces, wherein the material-removing cutting tool is equipped with piezoceramic transducers (22, 30, 33) in the form of sensors, actuators or pure voltage generators, wherein these transducers are arranged at at least one location on the cutting tool or on its bearing arrangement, at which location at least one component (-F c, -F f, -F p) of the cutting force (-F) arising during the machining acts on the cutting tool, wherein the transducers (22, 30, 33) are connected to the control device of the machine tool, and the signals (23, 31, 34) generated in the transducers (22, 30, 33) as a result of the action of forces and utilized by the control device can be used for controlling the machining of the workpieces, wherein a) on the carrier a cutting element in the form of a cutting plate is fastened in a recess of the carrier in such a manner that a controlled movement with respect to the carrier is possible, and the carrier is likewise fastened in a tool holder in a recess in such a manner that a controlled movement with respect to the tool holder is possible, b) the piezoceramic transducers (22, 30, 33) are arranged both between the cutting element and the carrier of the cutting tool and between the carrier of the cutting tool and the tool holder and are supported in recesses, c) positioned against the cutting element and also the carrier there are firstly sensors which are intended to determine the forces acting on the cutting element or the tool holder respectively and therefore on the machine tool, and these sensors are single-layer piezo elements, d) arranged between the sensors and the carrier and between the sensors and the tool holder, separated from one another by an insulating support plate, there are transducers in the form of voltage generators, and these are multi-layer elements, e) arranged on the cutting element between the voltage generators and the carrier there are actuators, likewise separated by an insulating support plate, and these actuators are multi-layer elements, f) the actuators are arranged in the tool holder in such a manner that, taking account of the type of construction, a maximum force can be exerted on the carrier, wherein they are surrounded concentrically by the sensors and voltage generators. a) on the carrier a cutting element in the form of a cutting plate is fastened in a recess of the carrier in such a manner that a controlled movement with respect to the carrier is possible, and the carrier is likewise fastened in a tool holder in a recess in such a manner that a controlled movement with respect to the tool holder is possible, b) the piezoceramic transducers (22, 30, 33) are arranged both between the cutting element and the carrier of the cutting tool and between the carrier of the cutting tool and the tool holder and are supported in recesses, c) positioned against the cutting element and also the carrier there are firstly sensors which are intended to determine the forces acting on the cutting element or the tool holder respectively and therefore on the machine tool, and these sensors are single-layer piezo elements, d) arranged between the sensors and the carrier and between the sensors and the tool holder, separated from one another by an insulating support plate, there are transducers in the form of voltage generators, and these are multi-layer elements, e) arranged on the cutting element between the voltage generators and the carrier there are actuators, likewise separated by an insulating support plate, and these actuators are multi-layer elements, f) the actuators are arranged in the tool holder in such a manner that, taking account of the type of construction, a maximum force can be exerted on the carrier, wherein they are surrounded concentrically by the sensors and voltage generators.