The influence of quantum electrodynamics in heavy ions is demonstrated. The contributions to the Lamb shift in hydrogen-like uranium are outlined, and quantum electrodynamical corrections to the radiative electron capture (REC) are investigated in the region of highly relativistic projectile energies by modifying the wave functions according to the Uehling potential. Exact relativistic calculations are employed for the radiative recombination. The deviation from non-QED calculations is found to amount to up to 2% in U⁹²⁺ for a projectiles energy of 10 GeV/u and forward emission angles of the emitted photon.