Construction and classification of Coulomb branch geometries

We give a non-technical summary of the classification program, very dear to the hearts of both authors, of four dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) based on the study of their Coulomb branch geometries. We outline the main ideas behind this program, review the most important results thus far obtained, and the prospects for future results. This contribution will appear in the volume "the Pollica perspective on the (super)-conformal world" but we decided to also make it available separately in the hope that it could be useful to those who are interested in obtaining a quick grasp of this rapidly developing program.