Most models of new physics contain extended Higgs sectors with multiple Higgs bosons. The observation of an additional Higgs boson, besides the ~125 GeV one already discovered, will thus serve as an irrefutable evidence of physics beyond the Standard Model. However, even when fairly light, these additional Higgs bosons may have escaped detection at LEP, Tevatron and LHC hitherto, owing to their highly reduced couplings to the SM particles. Therefore, in addition to the searches based on their conventional production processes, such as gluon or vector boson fusion, possible new search modes need ! to be exploited at collider experiments in order to establish their signatures. I will discuss the phenomenology of such exotic Higgs bosons with masses ranging from a few GeV to about 150 GeV, in the Next-to-Minimal Supersymmetric SM and the Type-I 2-Higgs Doublet Model, in some such atypical search channels at the LHC.