This paper presents a study of Z→llγ decays with the ATLAS detector at the Large Hadron Collider. The analysis uses a proton–proton data sample corresponding to an integrated luminosity of 20.2 fb-1 collected at a centre-of-mass energy s = 8 TeV. Integrated fiducial cross-sections together with normalised differential fiducial cross-sections, sensitive to the kinematics of final-state QED radiation, are obtained. The results are found to be in agreement with state-of-the-art predictions for final-state QED radiation. First measurements of Z→llγγ decays are also reported.