The long-sought Higgs Boson has been finally found in the CERN Large Hadron Collider (LHC), which was a milestone for the community of particle physics. However, the standard model (SM) of the elementary particles has no answer to all the phenomena observed in nature. For instance, this theory cannot explain the neutrino oscillation puzzle, the origin neutrino masses, the flavor problem, etc. For this reason, it is important to study processes that can show us evidence of physics beyond the SM. With this aim, we will study some exotic Higgs decays in the SM and some extension theories, which could be at the reach of experimental detection and can help us to a better understanding of the properties of this particle. In particular, we are interested in the decays H-> Z,gamma, H -> Z,gamma,gamma, H->Zgg. In the SM, these decays are highly suppressed but their decay widths can be significantly enhanced in some extension models, such as supersymmetric models, little Higgs models, etc. These kind of decays can impose constraints on the parameters of these extension models.