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Free form surfaces are used in various applications, such as in the aviation industiy, in the medicine, or for tool and die making. Compressor blades as well as knee prostheses and dies have complex curved surfaces. Five-axis grinding is a possibility to machine such curved swfaces in a high shape accuracy and surface quality. The use of this technology depends on a high degree of the operational background. Furthermore, the complexity of the tool path generation requires the use of computer-aided design/computer aided manufacturing {CAD/CAM) systems. This technical review gives an overview about state of the art of five-axis grinding and presents results, which can close some scientific lacks. Models were developed to predict the surface roughness and material removal dependent on the process parameters. Additionally, the relationship between tool geometry, shape accuracy as well as contact conditions is discussed. How to Grind With Five-Axis?Workpieces become more and more complex due to improving function, optic or haptic as well as downsizing of dimensions. These workpieces are often made of materials, which are difficult to machine. For example, complex shaped knee implants out of wear-resistant biocompatible oxide ceramics or forging dies for crankshafts reinforced by ceramic inlays [1,2]. Double curved or free formed surfaces can be ground with three-or five-axis kinematic. By applying three-axis kinematic, toric grinding wheels move line by line over the surface, whereby the tool axes are always parallel to machine tool axes [3]. However, profitability and precision of the three-axis manufacturing are limited. Changing workpiece curvatures leads to varying contact conditions and decreasing shape accuracy. In contrast to three-axis kinematic, five-axis machine tools have three translational axes (X, Y, and Z) and two additional rotational axis. These axes enable a simultaneous rotation and tilling of the tool relative to the surface of the workpiece [4,5]. As a result, the grinding wheel axis can always be oriented vertically to the normal vector of the surface and the variation of the contact conditions is reduced. Moreover, due to the high kinematic flexibility of five-axis manufacturing, undercuts as well as complex free formed surfaces are machined with high precision [6], Five-axes processes enable machining within