A brief review on unconventional oxygen-isotope (16O/18O) effects (OIE) in cuprate high-temperature superconductors (HTS) is presented. First the doping dependence of the OIE on the superconducting transition temperature TC in various HTS is discussed. For all cuprate HTS families the OIE exponent of TC (αO) shows a generic trend: In the underdoped regime αO is large (αO > 0.5) and becomes small in the optimally doped and overdoped regime. Magnetization, magnetic torque, and muon-spin rotation OIE studies of the in-plane penetration depth λab(0) in doped La2-xSrxCuO4 and Y1-xPrxBa2Cu3O7-δ indicate a substantial oxygen-mass dependence of the quantity λab-2(0), proportional to the superfluid density ρs(0) which increases with reduced doping. Even at optimal doping, where the OIE on TC is small, a pronounced OIE on λab(0) is present . Note that an OIE on the penetration depth is not expected for a conventional phonon-mediated superconductor (for which the Migdal adiabatic approximation holds). The oxygen-isotope shifts of TC and λab(0) exhibit a correlation that appears to be generic for various families of HTSC. Site-selective OIE investigations of Y1-xPrxBa2Cu3O7-δ clearly reveal that the planar oxygen atoms mainly contribute to the total OIE on TC as well as on λab(0) at all doping levels. These unusual isotope effects strongly suggest that lattice effects play an essential role in the basic physics of cuprate HTS and have to be considered in any realistic theoretical model.
 R. Khasanov et al., Phys. Rev. Lett. 92, 057602-1 (2004).