Laser surface texturing (LST) is one of the most promising technologies for controllable surface structuring and the acquisition of specific physical surface properties needed in functional surfaces. The quality and processing rate of the laser surface texturing strongly depend on the correct choice of a scanning strategy. In this paper, a comparative review of the classical and recently developed scanning strategies of laser surface texturing is presented. The main attention is paid to maximal processing rate, precision and existing physical limitations. Possible ways of further development of the laser scanning strategies are proposed.