The industrial applications of the technology of laser-beam surface hardening by remelting grey and nodular graphite cast irons, low-carbon steel, and of aluminium alloys with silicon result in shorter times of heat treatment and lower costs of treatment. For laser remelting, a physical-mathematical description of temperature cycles in heating and cooling (this is referred to in a manual on laser-beam treatment published by the American Laser Institute) was developed. Such a description of the temperature cycles permits easier and more correct determination of optimum conditions of hardening by remelting. An expert system was elaborated to optimize the conditions on the basis of the experimental results and by means of the physical-mathematical model of hardening by remelting with special regard to the mode of laser-beam guidance across the workpiece surface in terms of a minimum magnitude of deformations and compressive residual stresses. A mathematical model for the optimization of laser cutting of low-carbon steel was elaborated for MPP Maribor in terms of assuring cut quality and minimum product deformations. Criteria of on-line optimization of the laser-cutting process in terms of the selection of the cutting conditions based on IR radiation from the cutting front were developed. It was proved with numerous experiments that it was possible to obtain the required microstructure reinforced by precipitates at the nano level by applying laser repair welding or surfacing and laser precipitation hardening, which is a contribution to the knowledge of laser-beam treatment of the steel concerned. Quenching was studied using polymeric water solutions of different concentrations and quenching oils. A new experimental equipment was used, for the first time worldwide, to investigate the phenomena at the boundary between the workpiece and a cooling medium using a hydrophone. An analysis of acoustic emission was employed to select the most suitable cooling medium ensuring the repeatability of results of heat treatment, i.e., the same variations of hardness and residual stresses in steel. The experimental method is original and new and permits a good control of the quenching process in common cooling media and in polymeric water solutions with different concentrations. A paper sent to a specialised conference "Quenching & Distortion" (Beijing 2003) is being reviewed. When presented at the conference, it aroused a great interest. We were consulted by numerous research workers on more detailed data on the experimental equipment such as manufacturers and prices of individual system elements. We also obtained a new invitation from one of the editors of a well-known journal of ASTM to present the latest findings as a sound track presenting quenching of steel. The advancements in non-destructive testing methods based on the magnetic Barkhausen noise include the development of new sensors and different techniques of measuring the state of a material and a technique of measuring residual stresses. The investigation is beneficial to individual, small-series and large-series control of parts where 100% quality control is required. In non-destructive testing of materials based on the magnetic Barkhausen noise, making reference to achievements on the international level, special attention may be paid to the development and testing of "mini" sensors and their adaptability to various shapes of machine parts. In addition to the "mini" sensors a new and original method of determining residual stresses based on the Barkhausen noise was developed. The method is original, very simple and rapid. It makes it possible to determine residual stresses at workpiece surfaces as well as the through-depth variation of residual stresses in a hardened layer. The development of our sensors for micromagnetic testing aroused wide interest of researchers in this field. An agreement was reached with a research group of Prof. Nardoni from the University of