  The spin-orbit Mott insulator Sr${}_2$IrO${}_4$ has attracted a lot of
interest in recent years from theory and experiment due to its close connection
to isostructural high-temperature copper oxide superconductors. Despite of not
being superconducting its spectral features closely resemble those of the
cuprates, including Fermi surface and pseudogap properties. In this article, we
review and extend recent work in the theoretical description of the spectral
function of pure and electron-doped Sr${}_2$IrO${}_4$ based on a cluster
extension of dynamical mean-field theory ("oriented-cluster DMFT") and compare
it to available angle-resolved photoemission data. Current theories provide
surprisingly good agreement for pure and electron-doped Sr${}_2$IrO${}_4$, both
in the paramagnetic and antiferromagnetic phases. Most notably, one obtains
simple explanations for the experimentally observed steep feature around the
$M$ point and the pseudo-gap-like spectral feature in electron-doped
Sr${}_2$IrO${}_4$.
