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[Formula: see text], 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 [Formula: see text], 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 [Formula: see text] for 10 GeV [Formula: see text] 62 GeV. Limits are also presented for Higgs boson-like scalars (H) for [Formula: see text] 125 GeV, and for a [Formula: see text] decaying to three photons via [Formula: see text]. Additionally, the observed limit on the branching ratio of the Z boson decay to three photons is found to be BR[Formula: see text], a result five times stronger than the previous result from LEP.