This talk is devoted to selected rational techniques which are used in geometric modelling and other related CAx. When the computers became available that allowed machining of 3D shapes, it appeared a necessity to define a computer-compatible description of those shapes. The most promising representation was soon identified to be in forms of parametric curves and surfaces. Hence, exploring the history of Computer Aided Geometric Design in industrial and related applications we can clearly see that study of rational techniques and rational representations were at the very foundation of geometric modelling. However, although Computer Aided Geometric Design and consequently a vast variety of geometrical applications is based on parametric piecewise rational representations, the major problem of CAGD is that many natural geometrical operations do not preserve rationality of derived objects (among the most frequent such operations belong offsetting, operation of convolution and Minkowski sums).