In this seminar, I overview the research work carried out by IMATI-CNR on the extension of the Hough transform (HT) to recognize families of planar and spatial curves and surface primitives on 3D objects and point clouds. Recent developments are transforming the HT into a tool computationally affordable even outside the classical context of recognition of lines, circles and ellipses in the plane and planes and spheres in the space. In particular, I will focus on some applications such as the characterization of curves and complex patterns on artefacts and the creation of geometric models with curvilinear elements.