One of the important applications of extended discretization methods concerns shape and topology optimization.  Numerical methods relying on traditional body-fitted meshes can be impractical when the geometry itself is the principal unknown: the use of remeshing or mesh deformation tools can be inefficient, plagued with robustness problems, and impose limitations on the set of admissible geometries so that the best designs become unattainable. It is therefore of great interest to bring the new developments of extended discretization methods to the attention of the practitioners of shape and topology optimization. It is also of high interest for developers of extended discretization methods to become aware of the whole spectrum of optimization problems in which improved discretization methods could facilitate the algorithms.  The purpose of this minisymposium is to help bridging the gap between researchers involved in extended discretization methods and shape and topology optimization experts.  The session welcomes contributions in methods development as well as applications of shape and topology optimization, not necessarily involving extended discretization methods. However, contributions that do use such methods are of course of particular interest.