X-ray and neutron scattering studies of the lead-based family of perovskite relaxors Pb(Zn_1/3Nb_2/3)O₃-xPbTiO₃ (PZN-xPT) and Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-xPT) have documented a highly unusual situation in which the near-surface region of a single crystal can exhibit a structure that is different from that of the bulk when cooled to low temperatures. The near-surface region, or “skin” can also display critical behavior that is absent in the crystal interior, as well as a significantly different lattice spacing. By varying the incident photon energy, and thus the effective penetration depth, X-ray measurements indicate a skin thickness of order 10-50 µm for PZN-xPT samples with 0 ≤ x ≤ 8%. Neutron residual stress measurements on a large PMN single crystal reveal a uniform lattice spacing within the bulk, but an increased strain near the surface. The presence of this skin effect has led to incorrect phase diagrams for both the PZN-xPT and PMN-xPT systems and erroneous characterizations of the nature of the relaxor state.