Searches for exotic decays of the Standard Model (SM) Higgs boson and for evidence of additional beyond the SM Higgs-like particles provide fundamental tests of the SM theory, leading to possible indications of new physics mechanisms. The latest results from the ATLAS and CMS Collaborations are presented. The analyses are performed in a wide range of topologies, using proton-proton collision data collected with the two multi-purpose detectors at the LHC at a centre-of-mass energy $\sqrt{s}$ = 13 TeV, with an integrated luminosity up to 139 fb$^{-1}$. No evidence for new physics processes is found, thus setting exclusion limits on the various models.