I will review popular minimal singlet and doublet scalar extensions of
the Standard Model with viable Dark Matter candidates. After satisfying relic density conditions, these models are further constrained by direct and indirect detection experiments and by LHC data.
Moreover, if one introduces CP violation in the scalar sector, the bounds from Electric Dipole Moment experiments limit the model further.
I will then motivate 3-Higgs-Doublet Models and show that such models can accommodate Dark Matter candidates and CP violation in the scalar sector simultaneously while surviving all experimental and theoretical bounds. I will then present "smoking gun" signatures of such models at the LHC.