First-principles calculation of electron-phonon (e-ph) coupling is of tremendous interest as it serves as a nonempirical approach to predict and understand a number of phenomena. In this talk, we will present a new ab initio linear-response method named GW perturbation theory (GWPT) that computes the e-ph interaction with the full inclusion of the GW nonlocal, energy-dependent self-energy effects, going beyond the standard density-functional perturbation theory, which has been shown to be inadequate in many materials. We apply GWPT to study electron-phonon interaction in oxide superconductors. We first show that the e-ph interaction in Ba1-xKxBiO3 is significantly enhanced by many-electron correlations, and is strong enough to explain its high superconducting Tc of 32 K as well as its doping dependence. Secondly, we study the 70-meV photoemission nodal kink in cuprates whereas its origin is under debate. Ab initio results on a prototypical cuprate La2-xSrxCuO4 reveal that the correlation-enhanced e-ph interaction gives rise to strong nodal kinks in quantitative agreement with experiments.