  We report on recent theoretical advances in the description of the $pp\to
t\bar{t}W$ process. First, we discuss a comparison of many state-of-the-art
predictions for multi-lepton signatures including the leading QCD contributions
at $\mathcal{O}(\alpha_s^3\alpha^6)$ as well as subleading EW contributions at
$\mathcal{O}(\alpha_s\alpha^8)$. Furthermore, we briefly discuss recent
improvements using multi-jet merging techniques.
