The three-dimensional plasma boundary displacements induced by applied non-axisymmetric magnetic perturbations have been measured in ASDEX Upgrade, DIII-D, JET, MAST and NSTX. The displacements arising from applied resonant magnetic perturbations (RMPs) are measured up to ±5% of the minor radius in present-day machines. Good agreement can be found between different experimental measurements and a range of models—be it vacuum field line tracing, ideal three-dimensional MHD equilibrium modelling, or nonlinear plasma amplification. The agreement of the various experimental measurements with the different predictions from these models is presented, and the regions of applicability of each discussed. The measured displacement of the outboard boundary from various machines is found to correlate approximately linearly with the applied resonant field predicted by vacuum modelling (though it should be emphasized that one should not infer that vacuum modelling accurately predicts the displacement inside the plasma). The RMP-induced displacements foreseen in ITER are expected to lie within the range of those predicted by the different models, meaning less than ±1.75% (±3.5 cm) of the minor radius in the H-mode baseline and less than ±2.5% (±5 cm) in a 9 MA plasma. Whilst a displacement of 7 cm peak-to-peak in the baseline scenario is marginally acceptable from both a plasma control and heat loading perspective, it is important that ITER adopts a plasma control system which can account for a three-dimensional boundary corrugation to avoid an n = 0 correction which would otherwise locally exacerbate the displacement caused by the applied fields.