An apparatus (10; 110) for machining a workpiece, in particular a workpiece provided with cutting edges, by means of a grinding or erosion tool (34; 150), the apparatus (10; 110) comprising: - a base (12; 112), - a workpiece carrier (14; 114) comprising a receiving device (16; 116) for receiving a workpiece, and - a machining device (18; 118) compising the grinding or erosion tool (34; 150) that is used for machining and has a tool axis (A; B), wherein the receiving device (16; 116) together with the workpiece received therein is rotatable about a first axis of rotation of the receiving device (16; 116) and is arranged on a slide assembly (22; 122) comprising a first linear slide that is displaceable along a first linear axis associated with the first linear slide and running parallel to the axis of rotation, and comprising a second linear slide that is displaceable along a second linear axis associated with the second linear slide and running transversely to the axis of rotation and transversely to the first linear axis; wherein the workpiece carrier (14; 114) together with the associated slide assembly (22; 122) and the machining device (18; 118) are rotatable relative to one another about a second axis of rotation that is transverse to the first axis of rotation and transverse to the tool axis (A; B), characterized in that the slide assembly (22; 122) is displaceable relative to the base (12; 112) along a third linear axis that is transverse to the first and second linear axes (X, Y), and that the apparatus (10; 110) is configured to rotate the receiving device (16; 116) about the first axis of rotation and/or to rotate the workpiece carrier (14; 114) about the second axis of rotation and/or to relatively rotate the machining device (18; 118) about the second axis of rotation in mutual dependence such that, during machining, a current machining position in which the machining point of the grinding or erosion tool (34; 150) is located on a surface of the workpiece to be machined is on the second axis of rotation. - a base (12; 112), - a workpiece carrier (14; 114) comprising a receiving device (16; 116) for receiving a workpiece, and - a machining device (18; 118) compising the grinding or erosion tool (34; 150) that is used for machining and has a tool axis (A; B), wherein the receiving device (16; 116) together with the workpiece received therein is rotatable about a first axis of rotation of the receiving device (16; 116) and is arranged on a slide assembly (22; 122) comprising a first linear slide that is displaceable along a first linear axis associated with the first linear slide and running parallel to the axis of rotation, and comprising a second linear slide that is displaceable along a second linear axis associated with the second linear slide and running transversely to the axis of rotation and transversely to the first linear axis; wherein the workpiece carrier (14; 114) together with the associated slide assembly (22; 122) and the machining device (18; 118) are rotatable relative to one another about a second axis of rotation that is transverse to the first axis of rotation and transverse to the tool axis (A; B), characterized in that the slide assembly (22; 122) is displaceable relative to the base (12; 112) along a third linear axis that is transverse to the first and second linear axes (X, Y), and that the apparatus (10; 110) is configured to rotate the receiving device (16; 116) about the first axis of rotation and/or to rotate the workpiece carrier (14; 114) about the second axis of rotation and/or to relatively rotate the machining device (18; 118) about the second axis of rotation in mutual dependence such that, during machining, a current machining position in which the machining point of the grinding or erosion tool (34; 150) is located on a surface of the workpiece to be machined is on the second axis of rotation.