  Building on recent progress in the study of compactifications of $6d$ $(1,0)$
superconformal field theories (SCFTs) on Riemann surfaces to $4d$
$\mathcal{N}=1$ theories, we initiate a systematic study of compactifications
of $5d$ $\mathcal{N}=1$ SCFTs on Riemann surfaces to $3d$ $\mathcal{N}=2$
theories. Specifically, we consider the compactification of the so-called rank
1 Seiberg $E_{N_f+1}$ SCFTs on tori and tubes with flux in their global
symmetry, and put the resulting $3d$ theories to various consistency checks.
These include matching the (usually enhanced) IR symmetry of the $3d$ theories
with the one expected from the compactification, given by the commutant of the
flux in the global symmetry of the corresponding $5d$ SCFT, and identifying the
spectrum of operators and conformal manifolds predicted by the $5d$ picture. As
the models we examine are in three dimensions, we encounter novel elements that
are not present in compactifications to four dimensions, notably Chern-Simons
terms and monopole superpotentials, that play an important role in our
construction. The methods used in this paper can also be used for the
compactification of any other $5d$ SCFT that has a deformation leading to a
$5d$ gauge theory.
