We consider effects of strong electromagnetic fields in collisions of ultra-relativistic nuclei at the RHIC and LHC colliders. Since the parameter $Z\alpha$ is not small ($Z\alpha \approx 0.6$ for Au-Au and Pb-Pb collisions), the whole series in $Z\alpha$ has to be summed in order to obtain the cross section with sufficient accuracy. For the production of $e^+e^-$ and $\mu^+\mu^-$ pairs we present new results related to the Coulomb corrections (corresponding to multi-photon exchange of the produced leptons with the nuclei) and to the unitarity corrections (corresponding to the exchange of light-by-light blocks between nuclei). For nuclear bremsstrahlung we calculated the unitarity corrections and a special case related to the virtual Delbr\"uck scattering.