The search for non-standard, invisible or rare decays of the Higgs boson is an important area of investigation at the LHC because of the sensitivity to effects from physics beyond the Standard Model. In this article three recent measurements from the ATLAS Collaboration are presented; the search for Higgs boson decays to Zγ, the search for an invisibly decaying Higgs boson or dark matter candidate produced in association with a Z boson, and the search for Higgs boson decays to φγ and ργ.