  In recent years, $\gamma$-ray emission has been detected from star-forming
galaxies (SFGs) in the local universe, including M82, NGC 253, Arp 220 and M33.
The bulk of this emission is thought to be of hadronic origin, arising from the
interactions of cosmic rays (CRs) with the interstellar medium of their host
galaxy. Distant SFGs are presumably also bright in $\gamma$-rays. Although they
would not be resolvable as point sources, distant unresolved SFG populations
contribute $\gamma$-rays to the extra-galactic $\gamma$-ray background (EGB).
Despite the wealth of high-quality all-sky EGB data collected over more than a
decade of operation with the \textit{Fermi}-LAT $\gamma$-ray space telescope,
the exact contribution of SFGs to the EGB remains unsettled. In this study, we
model the $\gamma$-ray emission from SFG populations and demonstrate that such
emission can be characterized by just a small number of physically-motivated
parameters. We further show that source populations would leave anisotropic
signatures in the EGB, which could be used to yield information about the
underlying properties, dynamics and evolution of CR-rich SFGs.
