  We study extensions of the Standard Model (SM) in which copies of the SM
scalar SU(2) doublet are added to the Higgs sector. These scalar doublets
either acquire a Vacuum Expectation Value (VEV) and hence are active or do not
develop a VEV and are inert. We consider CP-violation (CPV) in both the active
and inert sector. As an example of a model with CPV in the active sector, we
present a Type-I 2-Higgs-Doublet Model (2HDM) with two active doublets and show
Large Hadron Collider (LHC) signals of such a scenario. The amount of CPV in
this case is very limited due to constraints coming from Electric Dipole Moment
experiments. Moreover, 2HDMs with only active doublets do not provide a Dark
Matter (DM) candidate. As a result, we turn to 3-Higgs-Doublet Models (3HDMs)
where unbounded CPV and viable DM candidates could be introduced simultaneously
in the inert sector. We investigate DM phenomenology of such models.
