In this talk I will describe how to systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d N=(1,0) SCFTs. Such 5d theories have a realization in M-theory on a singular Calabi-Yau threefold. To obtain a 5d SCFT from 6d, after circle reduction one needs to mass deform the theory and decouple a particular sector. There are two different types of decoupling. In terms of the IR gauge theory descriptions, one corresponds to decoupling flavor hypermultiplets, the other to decouple an entire gauge sector. The former is applicable to reductions of very Higgsable theories, whereas the latter is usually required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In particular, this case in M-theory corresponds to the decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify I will show how this works for 5d SCFTs that descend from non-Higgsable clusters and minimal and non-minimal conformal matter theories. I will also describe how from these geometries we determine the so-called combined fiber diagrams (CFD) introduced in arXiv:1906.11820, arXiv:1907.05404, arXiv:1909.09128. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling.Finally, inspired by the tensor branch quiver structure of 6d theories, I will talk about a proposed useful gluing construction for 5d SCFTs from specific building blocks and their CFDs.
