The invention relates to a method and an apparatus for the laser machining of workpieces, a laser beam being two-dimensionally positionable with the aid of a laser machining head with respect to a surface of a workpiece and it being intended for the machining of the workpiece to take place with predeterminable contours. According to the object, it is to be possible for the forming of the contours to be realized with high positional accuracy at low cost and with little effort. To achieve this object, the laser beam is correspondingly guided by means of a laser machining head, in which at least one two-dimensionally pivotable scanner mirror is accommodated. The scanner mirror or two scanner mirrors is/are connected to an electronic evaluation and control unit. Before the actual machining, a set-actual value comparison is carried out with respect to the position of the workpiece with at least one predetermined contour with respect to the laser machining head. For this purpose, a light beam of a light source is focused and directed via one or else two scanner mirror(s) onto the surface of the workpiece and deflected along at least one axis by pivoting at least one of the scanner mirrors. The light reflected from the workpiece surface passes via the scanner mirror or mirrors onto an optical detector and is focused onto the latter. Taking into account the respective pivoting angle of the scanner mirror(s), the measuring signals of this optical detector are fed to the electronic evaluation and control unit, so that the deflection of the laser beam can be controlled during the machining in dependence on the actual position of the contour ascertained in this way for the machining.