  The latest results in the search for rare and exotic Higgs boson decays in
proton-proton collision events collected with the CMS detector at the LHC are
presented. The searches are performed for several decay modes of Higgs boson
including $\mathrm{H}\rightarrow{\rm X (X \rightarrow2\ell)\gamma}$ ($X= {\rm
Z}, \gamma^* $ and $\ell={\rm e},\mu$), $\mathrm{H}\rightarrow{ \mu\mu / {\rm
e}{\rm e}}$, invisible decays, lepton flavour violating decays and Higgs decay
to light scalars or pseudo-scalars. No hint for new physics has been found from
the analyzed results with the full LHC run-1 data collected during 2011 and
2012 at $\sqrt{s}=7-8$ TeV and with the run-2 data at $\sqrt{s}=13$ TeV
collected during 2015 and 2016. Limits are set for all the searches which have
been performed by CMS.
