Search for non-standard and rare decays of the Higgs boson with the ATLAS detector

At the LHC, searches for rare and exotic decays of the Higgs boson constitute an excellent opportunity to look for new physics. Some theories predict exotic decays that are heavily suppressed in the Standard Model, such as the ones violating lepton flavor conservation. Other theories predict enhanced branching ratios for rare decay modes, such as the ones to a photon and a $Z$ boson, or to a photon and a meson. Recent searches performed with $\sqrt{s}=8~$TeV and $13~$TeV $pp$ collisions recorded by the ATLAS detector are presented.