Higgs rare and exotic decays

Several recent searches for exotic and rare decays of the Standard Model Higgs boson with the ATLAS and CMS detectors are presented. The searches are performed on $\sqrt{s}$=13 TeV proton-proton collisions data collected at the LHC between 2015 and 2018. The topics covered include searches for the Higgs boson decays into two pseudoscalars, $H\rightarrow aa$, in three different final states, $2b2\mu$, $4b$ and $2\mu2\tau$, search for lepton-flavour violating Higgs decays, $H\rightarrow \mu\tau / e\tau$, and search for a rare $H\rightarrow \ell\ell \gamma$ decay. ATLAS presents evidence for the $H\rightarrow \ell\ell \gamma$ rare decay, amounting to an observed significance of $3.2\sigma$.