  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.

High Energy Physics - Theory