High-temperature superconductivity in cuprates was discovered almost exactly 20 years ago, but a satisfactory theoretical explanation for this phenomenon is still lacking. The isotope effect has played an important role in establishing electron-phonon interaction as the dominant interaction in conventional superconductors. Here we present a unified picture of the oxygen isotope effect in cuprate superconductors based on a phonon-mediated d-wave pairing model within the Bardeen-Cooper-Schrieffer theory. We show that this model accounts for the magnitude of the isotope exponent as functions of the doping level as well as the variation between different cuprate superconductors. The isotope effect on the superconducting transition is also found to resemble the effect of pressure on the transition. These results indicate that the role of phonons should not be overlooked for explaining the superconductivity in cuprates.electron-phonon interaction ͉ high-temperature superconductivity ͉ pressure effect U nderstanding the high-temperature superconductivity in cuprate superconductors is at the heart of current research in solid-state physics. The isotope effect is an important experimental probe in revealing the underlying pairing mechanism of superconductivity. Early measurements (1) of the isotope effect on the superconducting transition temperature, T c , provided key experimental evidence for phonon-mediated pairing and supported strongly the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity in conventional materials. When hightemperature superconductivity was discovered in copper oxides, the oxygen isotope exponents, defined by ␣ ' ϪdlnT c /dlnM, with M being the isotopic mass, were promptly measured. The initial finding of the small value of ␣ in La 1.85 Sr 0.15 CuO 4 (2, 3) and near zero value in YBa 2 Cu 3 O 7Ϫ␦ (␦ ϳ 0) (4-6) was taken to be convincing evidence against electron-phonon interaction as the dominant mechanism in these materials. However, later experiments have revealed a much richer and more complex situation (7). There is a striking variation of ␣ with doping level in a given cuprate material (8-11). Meanwhile, ␣ also varies among various compounds of different cuprate families (7,12). Interestingly, ␣ is a remarkably monotonic function of the number of CuO 2 layers in a way opposite to T c in optimally doped compounds (12). Such elaborate isotope effects strongly suggest that one should include phonons in the theory of high-T c superconductivity. Studies of neutron scattering (13), angleresolved photoemission spectroscopy (14, 15), and scanning transmission electron microscopy (16) provide further evidence for phonons being an important player in the basic physics of high-T c superconductivity.Compared with isotope substitution, pressure has been realized not only to be another effective way to change T c for a superconductor (17) but also to yield information on the interaction causing the superconductivity. So far, the record high T c of 164 K was achieved under high pressure in HgBa 2 C...