  The complex two-Higgs doublet model is one of the simplest ways to extend the
scalar sector of the Standard Model to include a new source of CP-violation.
The model has been used as a benchmark model to search for CP-violation at the
LHC and as a possible explanation for the matter-antimatter asymmetry of the
Universe. In this work, we re-analyse in full detail the softly broken
$\mathbb{Z}_2$ symmetric complex two-Higgs doublet model (C2HDM). We provide
the code C2HDM_HDECAY implementing the C2HDM in the well-known HDECAY program
which calculates the decay widths including the state-of-the-art higher order
QCD corrections and the relevant off-shell decays. Using C2HDM_HDECAY together
with the most relevant theoretical and experimental constraints, including
electric dipole moments (EDMs), we review the parameter space of the model and
discuss its phenomenology. In particular, we find cases where large CP-odd
couplings to fermions are still allowed and provide benchmark points for these
scenarios. We examine the prospects of discovering CP-violation at the LHC and
show how theoretically motivated measures of CP-violation correlate with
observables.
