Results of a search for new phenomena in events with at least three photons are reported. Data from proton–proton collisions at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb−1−1, were collected with the ATLAS detector at the LHC. The observed data are well described by the Standard Model. Limits at the 95 % confidence level on new phenomena are presented based on the rate of events in an inclusive signal region and a restricted signal region targeting the rare decay Z→3γZ→3γ, as well as di-photon and tri-photon resonance searches. For a Standard Model Higgs boson decaying to four photons via a pair of intermediate pseudoscalar particles (a), limits are found to be σ× BR (h→aa)× BR (a→γγ)2<10−3σSMσ× BR (h→aa)× BR (a→γγ)2<10−3σSM for 10 GeV <ma<<ma< 62 GeV. Limits are also presented for Higgs boson-like scalars (H) for mH>mH> 125 GeV, and for a Z′Z′ decaying to three photons via Z′→a+γ→3γZ′→a+γ→3γ. Additionally, the observed limit on the branching ratio of the Z boson decay to three photons is found to be BR(Z→3γ)<2.2×10−6(Z→3γ)<2.2×10−6, a result five times stronger than the previous result from LEP.