Curves and Surfaces play a fundamental role in many fields, such as Computational Geometry, Computer Aided Design, Computer Graphics, Geometric Modeling to name a few. Consequently, softwares that provide functionalities to handle them are very important. The aim of this session is to facilitate communication between researchers who have developed or plan to develop mathematical software related to implicit or parametric curves and surfaces. The softwares could be, for instance, for handling arrangements of curves and surfaces, or visualizing them, or computing their cell decomposition, or using them as a tool in various applications. We welcome talks that highlight some of the mathematical and algorithmic challenges that are faced in designing softwares for curves and surfaces, and demonstrate some of the recent advances made in this direction.