In the light of a Higgs (doublet) discovery at the Large Hadron Collider and nothing else, we entertain the possibility that there are three Higgs doublets in Nature just like there are three generations of quarks and leptons (a possibility in fact foreseen in some flavour models). With this in mind, we review the phenomenology of generic 3-Higgs Doublet Models (3HDMs) when one or more of the doublets are inert, so as to also have one or more (scalar) Dark Matter candidates.